Showing posts with label AlexSmola. Show all posts
Showing posts with label AlexSmola. Show all posts

Thursday, May 31, 2018

McKernel: A Library for Approximate Kernel Expansions in Log-linear Time - implementation -


Woohoo ! following up on a previous postJoachim lets me know of the release of an implementation:
Hi Igor,
The library is now up. The name changed to McKernel. Thanks for your interest.
https://github.com/curto2/mckernelhttps://arxiv.org/pdf/1702.08159
Cheers,
Curtó
Thanks !

Kernel Methods Next Generation (KMNG) introduces a framework to use kernel approximates in the mini-batch setting with SGD Optimizer as an alternative to Deep Learning. McKernel is a C++ library for KMNG ML Large-scale. It contains a CPU optimized implementation of the Fastfood algorithm that allows the computation of approximated kernel expansions in log-linear time. The algorithm requires to compute the product of Walsh Hadamard Transform (WHT) matrices. A cache friendly SIMD Fast Walsh Hadamard Transform (FWHT) that achieves compelling speed and outperforms current state-of-the-art methods has been developed. McKernel allows to obtain non-linear classification combining Fastfood and a linear classifier.

Implementation is here: https://github.com/curto2/mckernel





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Friday, July 29, 2016

Stochastic Frank-Wolfe Methods for Nonconvex Optimization

All the previous blog entries around the Frank-Wolfe can be found under this Frank-Wolfe tag.



We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However, our understanding of these algorithms in the nonconvex setting is fairly limited. In this paper, we propose nonconvex stochastic Frank-Wolfe methods and analyze their convergence properties. For objective functions that decompose into a finite-sum, we leverage ideas from variance reduction techniques for convex optimization to obtain new variance reduced nonconvex Frank-Wolfe methods that have provably faster convergence than the classical Frank-Wolfe method. Finally, we show that the faster convergence rates of our variance reduced methods also translate into improved convergence rates for the stochastic setting.
h/t Atlas Wang 


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Thursday, August 13, 2015

Cuckoo Linear Algebra






Cuckoo Linear Algebra by Li ZhouDavid G. Andersen , Mu Li , Alexander J. Smola



In this paper we present a novel data structure for sparse vectors based on Cuckoo hashing. It is highly memory efficient and allows for random access at near dense vector level rates. This allows us to solve sparse l1 programming problems exactly and without preprocessing at a cost that is identical to dense linear algebra both in terms of memory and speed. Our approach provides a feasible alternative to the hash kernel and it excels whenever exact solutions are required, such as for feature selection.

 
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Tuesday, June 16, 2015

Fast and Guaranteed Tensor Decomposition via Sketching

 


Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.
 
 
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Saturday, September 20, 2014

Wednesday, September 10, 2014

Randomized Nonlinear Component Analysis - implementation -




Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale.
In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements.
In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real-world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.
The implementation is here.

Let me note, something we pointed out earlier on Nuit Blanche:

It is of special interest that randomized algorithms are in many cases more robust than their deterministic analogues (Mahoney, 2011) because of the implicit regularization induced by randomness.
Indeed the seminal paper by Mike Mahoney was very clear on the advantages of randomization. Re-reading the introduction makes it plainly clear and is the basis for RandNLA (Randomized Numerical Linear Algebra)




(Submitted on 29 Apr 2011 (v1), last revised 15 Nov 2011 (this version, v3))

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many different research communities. This monograph will provide a detailed overview of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis. An emphasis will be placed on a few simple core ideas that underlie not only recent theoretical advances but also the usefulness of these tools in large-scale data applications. Crucial in this context is the connection with the concept of statistical leverage. This concept has long been used in statistical regression diagnostics to identify outliers; and it has recently proved crucial in the development of improved worst-case matrix algorithms that are also amenable to high-quality numerical implementation and that are useful to domain scientists. Randomized methods solve problems such as the linear least-squares problem and the low-rank matrix approximation problem by constructing and operating on a randomized sketch of the input matrix. Depending on the specifics of the situation, when compared with the best previously-existing deterministic algorithms, the resulting randomized algorithms have worst-case running time that is asymptotically faster; their numerical implementations are faster in terms of clock-time; or they can be implemented in parallel computing environments where existing numerical algorithms fail to run at all. Numerous examples illustrating these observations will be described in detail.



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Saturday, September 06, 2014

Saturday Morning Videos: Some ICML 2014 presentations.

There goes your saturday morning, here are some videos from the ICML meeting that might be of interest to the readers of Nuit Blanche:
N00228947.jpg was taken on September 03, 2014 and received on Earth September 04, 2014. The camera was pointing toward TITAN at approximately 2,484,614 miles (3,998,598 kilometers) away, and the image was taken using the CL1 and UV3 filters. 
Image Credit: NASA/JPL/Space Science Institute

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Monday, August 18, 2014

Fastfood: Approximate Kernel Expansions in Loglinear Time - The Paper -

Compressive sensing is not the only place where multiplying a vector or a matrix with a Gaussian matrix is a big deal for large scale problems (see the recent Random Matrices Are Too Damn Large ! and Another Comment on " Random Matrices Are Too Damn Large !"). If you recall this is also a problem for Random Kitchen Sinks, a randomized version of AdaBoost (a connection with compressive sensing is mentioned here). There, the training set in Machine Learning is used as a dictionary in order to learn a function. Those dictionaries are, however too large and the authors of the paper resort to a fast random projections to learn the function faster. 



We had the talk for over a year now, we now have the attendant paper. There is actually more in the paper than what was shown in the presentation earlier: Fastfood: Approximate Kernel Expansions in Loglinear Time by Quoc Viet Le, Tamas Sarlos, Alexander Johannes Smola

Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that storing and computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such computation significantly. Key to Fastfood is the observation that Hadamard matrices, when combined with diagonal Gaussian matrices, exhibit properties similar to dense Gaussian random matrices. Yet unlike the latter, Hadamard and diagonal matrices are inexpensive to multiply and store. These two matrices can be used in lieu of Gaussian matrices in Random Kitchen Sinks proposed by Rahimi and Recht (2009) and thereby speeding up the computation for a large range of kernel functions. Specifically, Fastfood requires O(n log d) time and O(n) storage to compute n non-linear basis functions in d dimensions, a significant improvement from O(nd) computation and storage, without sacrificing accuracy.
Our method applies to any translation invariant and any dot-product kernel, such as the popular RBF kernels and polynomial kernels. We prove that the approximation is unbiased and has low variance. Experiments show that we achieve similar accuracy to full kernel expansions and Random Kitchen Sinks while being 100x faster and using 1000x less memory. These improvements, especially in terms of memory usage, make kernel methods more practical for applications that have large training sets and/or require real-time prediction.


Related:


[6] Uniform Approximation of Functions with Random Bases, Ali Rahimi and Benjamin Recht
[8] Nystrom Method vs Random Fourier Features:: A Theoretical and Empirical Comparison Tianbao Yang, Yu-Feng Li, Mehrdad Mahdavi, Rong Jin, Zhi-Hua Zhou
[9 Pruning random features with correlated kitchen sinks -poster- Brian McWilliams and David Balduzzi

Tuesday, July 22, 2014

Context Aware Recommendation Systems ( Lei Tang, Xavier Amatriain)



Much like the presentation by Lei Tang (Wallmart Labs) on Adaptive User Segmentation for Recommendation at last year's GraphLab 2013 (see Slides (pdf) here and video here). Xavier Amatriain, of Netflix, made a presentation of what we should be expecting in terms of recommendation. The idea here is that most of this work cannot be static otherwise your customers just won't be responsive to it. Here are his slides and the attendant videos from the Machine Learning Summer School organized in Pittsburgh 2014 by Alex Smola. I note the focus put on matrix and tensor factorizations and the persistent reference to blog posts. It's a new world...more on that later.

Monday, July 21, 2014

Video Stream: GraphLab Conference 2014



We mentioned it before, the GraphLab conference is on and it is streamed live hereThe program is here (the Twitter tag seems to be #GraphLabConf )

Day 1: Monday, July 21, 2014General Admission. Registration opens at 8:00am.Session 
1: Data Product Pipeline in Practice
  • 9:00am Prof. Carlos Guestrin Co-Founder & CEO, GraphLab Keynote: GraphLab Strategy, Vision and Practice
  • 10:10am Baldo Faieta Social Computing Lead, Adobe Systems Algorithms for Creatives Talent Search using GraphLab
  • 10:30am Amit Moran Chief Data Scientist, Crosswise Customer Spotlight: Crosswise
  • 10:40am Coffee Break (20 mins)
Session 2: Data Science
  • 11:00am Alice Zheng Director of Data Science, GraphLab Machine Learning Toolkits in GraphLab Create
  • 11:20am Karthik Ramachandran, Erick Tryzelaar Lab41 Dendrite large scale graph analytics
  • 11:40am Tao Ye Sr. Scientist, Pandora Internet Radio Large scale music recommendation @ Pandora
  • 12:00pm Prof. Alex Smola CMU and Google Scaling Distributed Machine Learning with the Parameter Server
  • 12:20pm Jonathan Dinu Co-Founder, Zipfian Academy Customer Spotlight: Zipfian Academy
  • 12:30pm Lunch (70 mins)
Session 3: Data Engineering
  • 1:40pm Yucheng Low Co-Founder & Chief Architect, GraphLab Scalable Data Structures: SFrame & SGraph
  • 2:00pm Prof. Joe Hellerstein Co-Founder & CEO, Trifacta Data, DSLs and Transformation: Research and Practice
  • 2:20pm Reynold Xin Co-Founder, Databricks Unified Data Pipeline in Apache Spark
  • 2:40pm Wes McKinney Founder & CEO, DataPad Fast Medium Data Analytics at Scale
  • 3:00pm Coffee Break (20 mins)
Session 4: Deployment
  • 3:20pm Rajat Arya Senior Software Engineer, GraphLab Deployment with GraphLab Create
  • 3:40pm Milind Bhandarkar Chief Scientist, Pivotal The Zoo Expands: Labrador ♥ Elephant thanks to Hamster
  • 4:00pm Prof. Vahab Mirrokni Google Research ASYMP: Fault-tolerant Graph Mining via ASYnchronous Message Passing
  • 4:20pm Josh Wills Director of Data Science, Cloudera What Comes After The Star Schema?
  • 4:40pm Dr. Markus Weimer Microsoft Research REEF: Towards a Big Data stdlib
  • Session 5: Networking and Demos (5:00-7:00pm)



Day 2: Tuesday, July 22, 2014Training Admission. Registration opens at 8:00am.
GraphLab Create Hands-on Training
The goal of the day is to teach participants how to build a machine learning system at scale from prototype to production using GraphLab Create. A laptop is required to participate.
  • 9:30am Alice Zheng Director of Data Science, GraphLab Introduction
  • 9:45am Yucheng Low Co-Founder & Chief Architect, GraphLab Prepping Data for Analysis: Using GraphLab Create Data Structures and GraphLab Canvas
  • 10:30am Coffee Break (15 mins)
  • 10:45am Srikrishna Sridhar Data Scientist, GraphLab Supervised Learning: Regression and Classification
  • 11:15am Brian Kent Data Scientist, GraphLab Unsupervised Learning: Clustering, Nearest Neighbors, Graph Analysis
  • 11:45am Hands-on Training Exercises and Lunch
  • 1:45pm Chris Dubois Data Scientist, GraphLab Recommender Systems and Text Analysis
  • 2:15pm Coffee Break (15 mins)
  • 2:30pm Rajat Arya Sr. Software Engineer, GraphLab Deployment
  • 3:15pm Hands-on Training Exercises
  • 4:00pm Danny Bickson Co-Founder & Data Scientist, GraphLab Practical Data Science Tips
  • 4:45pm Alice Zheng Director of Data Science, GraphLab Closing Remarks




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Saturday, July 12, 2014

Saturday Morning Videos: Machine Learning Summer School Pittsburgh 2014, Muthu Muthukrishnan


Of note, Muthu was a recent speaker to our Paris/Europe Wide Machine Learning Meetup. RandNLA and Sketching/streaming are coming to ML fast and our meetup was at the forefront, Woohoo ! Here are the very interesting videos of Muthu, enjoy !

Tuesday, January 14, 2014

How Close is Compressive Sensing to Random Features with Random Kitchen Sinks?

I don't know but here is how the authors of [1] describe the Random KitcHen Sinks (RKS) for FastFood which are the non adaptive version of approaches like XNV. RKS seems to be a play on words for Reproducing Kernel Hilbert Spaces that one can use to approximate the identity (i.e. the reproducing property). From [1]

Random Kitchen Sinks (Rahimi & Recht, 2007;2008)1, the algorithm that our algorithm is based on, approximates the function f by means of multiplying the input with a Gaussian random matrix, followed by the application of a nonlinearity. If the expansion dimension is n and the input dimension is d (i.e., the Gaussian matrix is n x d), it requires O(nd) time and memory to evaluate the decision function f. For large problems with sample size mxn, this is typically much faster than the aforementioned \kernel trick" because the computation is independent of the size of the training set. Experiments also show that this approximation method achieves accuracy comparable to RBF kernels while offering significant speedup.

Potentially Interesting Reading


Deep neural networks are flexible models that are able to learn complex nonlinear functions of data. The goal of this project is to build a shallow neural network that has the same representational power as a deep network by learning an extra nonlinear feature transformation at each node. To apply these transformations, we borrow techniques from the area of scalable, approximate kernel methods. In particular, we use the Fastfood method introduced by Le at al. in [1], which allows an approximate feature map for a transition-invariate kernel to be computed in log-linear time. Our method learns an optimal Fastfood feature expansion at each node while simultaneously optimizing the weight parameters of the neural network. We demonstrate our method on multiple datasets and show that it has better classification performance than neural networks with similar architectures.
Image Credit: NASA/JPL/Space Science Institute
Full-Res: W00086165.jpg

W00086165.jpg was taken on January 12, 2014 and received on Earth January 12, 2014. The camera was pointing toward SATURN at approximately 1,457,373 miles (2,345,415 kilometers) away, and the image was taken using the MT3 and CL2 filters. 


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Thursday, December 05, 2013

#NIPS2013 papers, workshops ...

So #NIPS2013 is starting today with a set of tutorials, and a set of workshops listed below. Two words first, if you are prude or at work don't go watch the photos on Twitter (on your desktop) for the #NIPS2013 hashtag just yet! Second, for those of you in Paris next week, we'll have our 6th ML meetup. Third Andrej Karpathy has a nicer way of viewing the NIPS proceedings. It is here.

Without further due:

Here are a few papers I found interesting but the whole electronic proceeding is here (the whole pdf is here):

Several posters from the workshops are listed below:

    CONTRIBUTED TALKS

    • Mu Li, Li Zhou, Zichao Yang, Aaron Li, Fei Xia, David Andersen and Alexander Smola.
      Parameter Server for Distributed Machine Learning
      We propose a parameter server framework to solve distributed machine learning problems. Both data and workload are distributed into client nodes, while server nodes maintain globally shared parameters, which are represented as sparse vectors and matrices. The framework manages asynchronous data communications between clients and servers. Flexible consistency models, elastic scalability and fault tolerance are supported by this framework. We present algorithms and theoretical analysis for challenging nonconvex and nonsmooth problems. To demonstrate the scalability of the proposed framework, we show experimental results on real data with billions of parameters.
      PDF
    • Yarin Gal and Zoubin Ghahramani.
      Pitfalls in the use of Parallel Inference for the Dirichlet Process
      Recent work done by Lovell, Adams, and Mansingka [2012] and Williamson, Dubey, and Xing [2013] has suggested an alternative parametrisation for the Dirichlet process in order to derive non-approximate parallel MCMC inference for it. This approach to parallelisation has been picked-up and implemented in several different fields [Chahuneau et al., 2013, Pan et al., 2013]. In this paper we show that the approach suggested is impractical due to an extremely unbalanced distribution of the data. We characterise the requirements of efficient parallel inference for the Dirichlet process and show that the proposed inference fails most of these conditions (while approximate approaches often satisfy most of them). We present both theoretical and experimental evidence of this, analysing the load balance for the inference showing that it is independent of the size of the dataset and the number of nodes available in the parallel implementation, and end with preliminary suggestions of alternative paths of research for efficient non-approximate parallel inference for the Dirichlet process.
      PDF
    • Yingyu Liang, Maria-Florina Balcan and Vandana Kanchanapally.
      Distributed PCA and k-Means Clustering
      This paper proposes a distributed PCA algorithm, with the theoretical guarantee that any good approximation solution on the projected data for k-means clustering is also a good approximation on the original data, while the projected dimension required is independent of the original dimension. When combined with the distributed coreset-based clustering approach in [3], this leads to an algorithm in which the number of vectors communicated is independent of the size and the dimension of the original data. Our experiment results demonstrate the effectiveness of the algorithm.
      PDF

    POSTERS

    • Julien-Charles Lévesque, Christian Gagné and Robert Sabourin.
      Ensembles of Budgeted Kernel Support Vector Machines for Parallel Large Scale Learning
      In this work, we propose to combine multiple budgeted kernel support vector machines (SVMs) trained with stochastic gradient descent (SGD) in order to exploit large databases and parallel computing resources. The variance induced by budget restrictions of the kernel SVMs is reduced through the averaging of predictions, resulting in greater generalization performance. The variance of the trainings results in a diversity of predictions, which can help explain the better performance. Finally, the proposed method is intrinsically parallel, which means that parallel computing resources can be exploited in a straightforward manner.
      PDF
    • Zhen Qin, Vaclav Petricek, Nikos Karampatziakis, Lihong Li and John Langford.
      Efficient Online Bootstrapping for Large Scale Learning
      Bootstrapping is a useful technique for estimating the uncertainty of a predictor, for example, confidence intervals for prediction. It is typically used on small to moderate sized datasets, due to its high computation cost. This work describes a highly scalable online bootstrapping strategy, implemented inside Vowpal Wabbit, that is several times faster than traditional strategies. Our experiments indicate that, in addition to providing a black box-like method for estimating uncertainty, our implementation of online bootstrapping may also help to train models with better prediction performance due to model averaging.
      PDF
    • Arun Kumar, Nikos Karampatziakis, Paul Mineiro, Markus Weimer and Vijay Narayanan.
      Distributed and Scalable PCA in the Cloud
      Principal Component Analysis (CA) is a popular technique with many applications. Recent randomized PCA algorithms scale to large datasets but face a bottleneck when the number of features is also large. We propose to mitigate this issue using a composition of structured and unstructured randomness within a randomized PCA algorithm. Initial experiments using a large graph dataset from Twitter show promising results. We demonstrate the scalability of our algorithm by implementing it both on Hadoop, and a more flexible platform named REEF.
      PDF
    • Nedim Lipka.
      Towards Distributed Reinforcement Learning for Digital Marketing with Spark
      A variety of problems in digital marketing can be modeled as Markov decision processes and solved by dynamic programming with the goal of calculating the policy that maximizes the expected discounted reward. Algorithms, such as policy iteration, require a state transition and a reward model, which can be estimated based on a given data set. In this paper, we compare the execution times for estimating the transition function in a map-reduce fashion if the data set becomes large in terms of the number of records and features. Therefore, we create different-sized Spark and Hadoop clusters in the Amazon cloud computing environment. The in-memory clustering system Spark is outperforming Hadoop and runs up to 71% faster. Furthermore, we study the execution times of policy iteration running on Spark clusters and show the execution time reduction gained by increasing the number of instances in the cluster.
      PDF
    • Tuukka Ruotsalo, Jaakko Peltonen, Manuel J. A. Eugster, Dorota Glowacka, Giulio Jacucci, Aki Reijonen and Samuel Kaski.
      Lost in Publications? How to Find Your Way in 50 Million Scientific Documents
      Researchers must navigate big data. Current scientific knowledge includes 50 million published articles. How can a system help a researcher find relevant documents in her field? We introduce IntentRadar, an interactive search user interface and search engine that anticipates userâ™s search intents by estimating them form userâ™s interaction with the interface. The estimated intents are visualized on a radial layout that organizes potential intents as directions in the information space. The intent radar assists users to direct their search by allowing feedback to be targeted on keywords that represent the potential intents. Users can provide feedback by manipulating the position of the keywords on the radar. The system then learns and visualizes improved estimates and corresponding documents. IntentRadar has been shown to significantly improve usersâ™ task performance and the quality of retrieved information without compromising task execution time.
      PDF
    • Michael Kane and Bryan Lewis.
      cnidaria: A Generative Communication Approach to Scalable, Distributed Learning
      This paper presents a scalable, software framework that facilitates large-scale learning and numerical computing. Unlike existing MapReduce frameworks our design is not limited to embarrassingly parallel computing challenges. The framework sits on top of existing storage infrastructures and results of a computation may left out on the cluster (a reduce step is not required). Unlike existing distributed numerical frameworks the proposed framework is elastic and works with both dense and sparse data representations. This generality is achieved through a generative communication scheme whose expressions are either consumed by the distributed computing environment or used to move data, in a peer-to-peer (P2P) fashion, between nodes in a cluster/cloud. This approach integrates advances in the both cloud computing and the distributed numerical computing community and can be applied to a general class of learning challenges.
      PDF
    • Anshumali Shrivastava and Ping Li.
      Beyond Pairwise: Provably Fast Algorithms for Approximate k-Way Similarity Search
      We go beyond the notion of pairwise similarity and look into search problems with k-way similarity functions. In this paper, we focus on problems related to 3-way Jaccard similarity. We show that approximate R3way similarity search problems admit fast algorithms with provable guarantees, analogous to the pairwise case. Our analysis and speedup guarantees naturally extend to k-way resemblance. In the process, we extend traditional framework of locality sensitive hashing (LSH) to handle higher-order similarities, which could be of independent theoretical interest. The applicability of R3way search is shown on the Google Sets application as well as in an application for improving retrieval quality.
      PDF
    • Wei Dai, Jinliang Wei, Xun Zheng, Jin Kyu Kim, Seunghak Lee, Junming Yin, Qirong Ho and Eric Xing.
      Petuum: A System for Iterative-Convergent Distributed ML
      A major bottleneck to applying advanced ML programs at industrial scales is the migration of an academic implementation, often specialized for a small, wellcontrolled computer platform such as desktop PCs and small lab-clusters, to a big, less predicable platform such as a corporate cluster or the cloud. This poses enormous challenges: how does one train huge models with billions of parameters on massive data, especially when substantial expertise is required to handle many low-level systems issues? We propose a new architecture of systems components that systematically addresses these challenges, thus providing a generalpurpose distributed platform for Big Machine Learning. Our architecture specifically exploits the fact that many ML programs are fundamentally loss function minimization problems, and that their iterative-convergent nature presents many unique opportunities to minimize loss, such as via dynamic variable scheduling and error-bounded consistency models for synchronization. Thus, we treat data, parameter and variable blocks as computing units to be dynamically scheduled and updated in an error-bounded manner, with the goal of minimizing the loss function as quickly as possible.
      PDF
    • Haiqin Yang, Junjie Hu, Michael Lyu and Irwin King.
      Online Imbalanced Learning with Kernels
      Imbalanced learning, or learning from imbalanced data, is a challenging problem in both academy and industry. Nowadays, the streaming imbalanced data become popular and trigger the volume, velocity, and variety issues of learning from these data. To tackle these issues, online learning algorithms are proposed to learn a linear classifier via maximizing the AUC score. However, the developed linear classifiers ignore the learning power of kernels. In this paper, we therefore propose online imbalanced learning with kernels (OILK) to exploit the non-linearity and heterogeneity embedded in the imbalanced data. Different from previously proposed work, we optimize the AUC score to learn a non-linear representation via the kernel trick. To relieve the computational and storing cost, we also investigate different buffer update policies, including first-in-first-out (FIFO) and reservoir sampling (RS), to maintain a fixed budgeted buffer on the number of support vectors. We demonstrate the properties of our proposed OILK through detailed experiments.
      PDF
    • Alex Beutel, Abhimanu Kumar, Evangelos Papalexakis, Partha Pratim Talukdar, Christos Faloutsos and Eric Xing.
      FLEXIFACT: Scalable Flexible Factorization of Coupled Tensors on Hadoop
      Given multiple data sets of relational data that share a number of dimensions, how can we efficiently decompose our data into the latent factors? Factorization of a single matrix or tensor has attracted much attention, as, e.g., in the Netflix challenge, with users rating movies. However, we often have additional, side, information, like, e.g., demographic data about the users, in the Netflix example above. Incorporating the additional information leads to the coupled factorization problem. So far, it has been solved for relatively small datasets. We provide a distributed, scalable method for decomposing matrices, tensors, and coupled data sets through stochastic gradient descent on a variety of objective functions. We offer the following contributions: (1) Versatility: Our algorithm can perform matrix, tensor, and coupled factorization, with flexible objective functions including the Frobenius norm, Frobenius norm with an l1 induced sparsity, and non-negative factorization. (2) Scalability: FLEXIFACT scales to unprecedented sizes in both the data and model, with up to billions of parameters. FLEXIFACT runs on standard Hadoop. (3) Convergence proofs showing that FLEXIFACT converges on the variety of objective functions, even with projections.
      PDF
    • Faraz Makari Manshadi and Rainer Gemulla.
      A Distributed Approximation Algorithm for Mixed Packing-Covering Linear Programs
      Mixed packing-covering linear programs capture a simple but expressive subclass of linear programs. They commonly arise as linear programming relaxations of a number important combinatorial problems, including various network design and generalized matching problems. In this paper, we propose an efficient distributed approximation algorithm for solving mixed packing-covering problems which requires a poly-logarithmic number of passes over the input. Our algorithm is well-suited for parallel processing on GPUs, in shared-memory architectures, or on small clusters of commodity nodes. We report results of a case study for generalized bipartite matching problems.
      PDF
    • Artem Sokolov and Stefan Riezler.
      Task-driven Greedy Learning of Feature Hashing Functions
      Randomly hashing multiple features into one aggregated feature is routinely used in largescale machine learning tasks to both increase speed and decrease memory requirements, with little or no sacrifice in performance. In this paper we investigate whether using a learned (instead of a random) hashing function improves performance. We show experimentally that with increasing difference between the dimensionalities of the input space and the hashed space, learning hashes is increasingly useful compared to random hashing.
      PDF
    • Ahmed Elgohary, Ahmed Farahat, Mohamed Kamel and Fakhri Karray.
      Approximate Nearest Centroid Embedding for Kernel $k$-Means
      This paper proposes an efficient embedding method for scaling kernel k-means on cloud infrastructures. The embedding method allows for approximating the computation of the nearest centroid to each data instance and, accordingly, it eliminates the quadratic space and time complexities of the cluster assignment step in the kernel k-means algorithm. We show that the proposed embedding method is effective under memory and computing power constraints, and that it achieves better clustering performance compared to other approximations of the kernel kmeans algorithm.
      PDF
    • Yisheng Liao, Alex Rubinsteyn, Russell Power and Jinyang Li.
      Learning Random Forests on the GPU
      Random Forests are a popular and powerful machine learning technique, with several fast multi-core CPU implementations. Since many other machine learning methods have seen impressive speedups from GPU implementations, applying GPU acceleration to random forests seems like a natural fit. Previous attempts to use GPUs have relied on coarse-grained task parallelism and have yielded inconclusive or unsatisfying results. We introduce CudaTree, a GPU Random Forest implementation which adaptively switches between data and task parallelism. We show that, for larger datasets, this algorithm is faster than highly tuned multi-core CPU implementations.
      PDF
    • Shravan Narayanamurthy, Markus Weimer, Dhruv Mahajan, Tyson Condie, Sundararajan Sellamanickam and S. Sathiya Keerthi.
      Towards Resource-Elastic Machine Learning

      PDF
    • Ignacio Arnaldo, Kalyan Veeramachaneni and Una-May O'Reilly.
      Building Multiclass Nonlinear Classifiers with GPUs
      The adoption of multiclass classification strategies that train independent binary classifiers becomes challenging when the goal is to retrieve nonlinear models from large datasets and the process requires several passes through the data. In such scenario, the combined use of a search and score algorithm and GPUs allows to obtain binary classifiers in a reduced time. We demonstrate our approach by training a ten class classifier over more than 400K exemplars following the exhaustive Error Correcting Output Code strategy that decomposes into 511 binary problems.
      PDF
    • John Canny and Huasha Zhao.
      BIDMach: Large-scale Learning with Zero Memory Allocation
      This paper describes recent work on the BIDMach toolkit for large-scale machine learning. BIDMach has demonstrated single-node performance that exceeds that of published cluster systems for many common machine-learning task. BIDMach makes full use of both CPU and GPU acceleration (through a sister library BIDMat), and requires only modest hardware (commodity GPUs). One of the challenges of reaching this level of performance is the allocation barrier. While it is simple and expedient to allocate and recycle matrix (or graph) objects in expressions, this approach is too slow to match the arithmetic throughput possible on either GPUs or CPUs. In this paper we describe a caching approach that allows code with complex matrix (graph) expressions to run at massive scale, i.e. multi-terabyte data, with zero memory allocation after initial start-up. We present a number of new benchmarks that leverage this approach.
      PDF
    • Shohei Hido, Satoshi Oda and Seiya Tokui.
      Jubatus: An Open Source Platform for Distributed Online Machine Learning
      Distributed computing is essential for handling very large datasets. Online learning is also promising for learning from rapid data streams. However, it is still an unresolved problem how to combine them for scalable learning and prediction on big data streams. We propose a general computational framework called loose model sharing for online and distributed machine learning. The key is to share only models rather than data between distributed servers. We also introduce Jubatus, an open source software platform based on the framework. Finally, we describe the details of implementing classifier and nearest neighbor algorithms, and discuss our experimental evaluations.
      PDF

Accepted Papers


Poster presentations

Accepted Papers

Linear Bandits, Matrix Completion, and Recommendation Systems [pdf]
Efficient coordinate-descent for orthogonal matrices through Givens rotations [pdf][supplementary]
Improved Greedy Algorithms for Sparse Approximation of a Matrix in terms of Another Matrix [pdf]
Preconditioned Krylov solvers for kernel regression [pdf]
Probabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms [pdf][supplementary]
Dimension Independent Matrix Square using MapReduce [pdf]

  • Active Learning of Intuitive Sound Qualities (Huang, Duvenaud, Arnold, Partridge, and Oberholtzer) [pdf]
    There is often a mismatch between the high-level goals an artist wants to express and what the parameters of a synthesizer allow them to control. To enable composers to directly adjust personalized high-level qualities during sound synthesis, our system actively learns functions that map from the space of synthesizer control parameters to perceived levels of high-level qualities.
  • Automatic Construction and Natural-Language Summarization of Additive Nonparametric Models (Lloyd, Duvenaud, Grosse, Tenenbaum, and Ghahramani) [pdf][supplement1][supplement2]
    To complement recently introduced automatic model-construction and search methods, we demonstrate an automatic model-summarization procedure. After building an additive nonparametric regression model, our method constructs a report which visualizes and explains in words the meaning and relevance of each component. These reports enable human model-checking and the understanding of complex modeling assumptions and structure. We demonstrate this procedure on two time-series, showing that the automatically constructed models identify clearly interpretable structures that can be automatically described in simple natural language.
  • Designing Constructive Machine Learning Models based on Generalied Linear Learning Techniques (Kordjamshidi and Moens) [pdf]
    We propose a general framework for designing machine learning models that deal with constructing complex structures in the output space. The goal is to provide an abstraction layer to easily represent and design constructive learning models. The learning approach is based on generalized linear training techniques, and exploits techniques from combinatorial optimization to deal with the complexity of the underlying inference required in this type of models. This approach also allows to consider global structural characteristics and constraints over the output elements in an efficient training and prediction setting. The use case focuses on building spatial meaning representations from text to instantiate a virtual world.
  • Learning Graphical Concepts (Ellis, Dechter, Adams, and Tenenbaum) [pdf]
    How can machine learning techniques be used to solve problems whose solutions are best represented as computer programs? For example, suppose a researcher wants to design a probabilistic graphical model for a novel domain. Searching the space of probabilistic models automatically is notoriously difficult, especially difficult when latent variables are involved. However, researchers seem able to easily adapt commonly used modeling motifs to new domains. In doing so, they draw on abstractions such as trees, chains, grids and plates to constrain and direct the kinds of models they produce. This suggests that before we ask machine learning algorithms to discover parsimonious models of new domains, we should develop techniques that enable our algorithms to automatically learn these ?graphical concepts? in much the same way that researchers themselves do, by seeing examples in the literature. One natural way to think of these graphical concepts is as programs that take sets of random variables and produce graphical models that relate them. In this work, we describe the CEC algorithm, which attempts to learn a distribution over programs by incrementally finding program components that commonly help to solve problems in a given domain, and we show preliminary results indicating that CEC is able to discover the graphical concepts that underlie many of the common graphical model structures.
  • The Constructive Learning Problem: An Efficient Approach for Hypergraphs (Costa and Sorescu) [pdf]
    Discriminative systems that can deal with input graphs are known, however, generative/constructive approaches that can output (hyper)graphs belonging with high probability to a desired class, are less studied. Here we propose an approach that, differently from common graph grammars inference systems, is computationally efficient and robust to the presence of outliers in the training sample. We report experimental results in a de-novo molecular synthesis problem. We show that we can construct compounds that, once added to the original training set can improve the performance of a binary classification predictor.
  • Analyzing Probabilistic Models Generated by EDAs for Simplified Protein Folding Problems (Santana, Mendiburu, and Lozano) [pdf]
    Estimation of distribution algorithms (EDAs) are optimization methods that construct at each step a probabilistic graphical model (PGM) of the best evaluated solutions. The model serves as a concise representation of the regularities shared by the good solutions and can serve to unveil structural characteristics of the problem domain. In this paper we use the PGMs learned by EDAs in the optimization of 15, 575 instances of the hydrophobic-polar (HP) functional protein folding model to analyze the relationship between the information contained in the PGMs? structures and the quality of the EDA?s solutions.
  • Anticipating the Future By Constructing Human Activities using Object Affordances (Koppula and Saxena) [pdf]
    An important aspect of human perception is anticipation and anticipating which activities will a human do next (and how to do them) in useful for many applications, for example, anticipation enables an assistive robot to plan ahead for reactive responses in the human environments. In this work, we present a constructive approach for generating various possible future human activities by reasoning about the rich spatial-temporal relations through object affordances. We represent each possible future using an anticipatory temporal conditional random field (ATCRF) where we sample the nodes and edges corresponding to future object trajectories and human poses from a generative model. We then represent the distribution over the potential futures using a set of constructed ATCRF particles. In extensive evaluation on CAD-120 human activity RGB-D dataset, for new subjects (not seen in the training set), we obtain an activity anticipation accuracy (defined as whether one of top three predictions actually happened) of 75.4%, 69.2% and 58.1% for an anticipation time of 1, 3 and 10 seconds respectively. 1
  • Learning Global-to-Local Discrete Components with Nonparametric Bayesian Feature Construction (Heo, Lee, and Zhang) [pdf]
    Finding common latent components from data is an important step in many data mining applications. These latent variables are typically categorical and there are many sources of categorical variables, including dichotomous, nominal, ordinal, and cardinal values. Thus it is important to be able to represent the discrete components (categories) in a flexible way. Here we propose a nonparametric Bayesian approach to learning "plastic" discrete components by considering the uncertainty of the number of components with the Indian buffet processes (IBP). As observation models, we use the product of experts (PoE) to utilize sharper representation power and sparse over-completeness. We apply the proposed method to optical hand-written digit datasets and demonstrate its capability of finding flexible global-to-local components that can be used to describe and generate the observed digit images faithfully.
  • Racing Tracks Improvisation (Wang and Missura) [pdf][supplement]
    Procedural content generation is a popular technique in the game development. One of its typical applications is generation of game levels. This paper presents a method to generate tracks for racing games, by viewing racing track generation as a discrete sequence prediction problem. To solve it we combine two techniques from music improvisation. We show that this method is capable of generating new racing tracks which appear to be interesting enough.
  • STONES: Stochastic Technique for Generating Songs (Kamp and Manea) [pdf]
    We propose a novel approach for automatically constructing new songs from a set of given compositions that involves sampling a melody line as well as the corresponding harmonies given by chords. The song is sampled from a hierarchical Markov model that captures the implicit properties of good composed songs from a set of existing ones. We empirically show that songs generated by our approach are closer to music composed by humans than those of existing methods.
  • Constructing Cocktails from a Cocktail Map (Paurat, Garnett, and Gärtner) [pdf]
    Consider a dataset that describes cocktails by the amount of ingredients used and a lower dimensional embedding of it that can be considered a map of cocktails. The problem we tackle is to query an arbitrary point of interest in this lower dimensional embedding and retrieve a newly constructed cocktail which embeds to that queried location. To do so, we formulate the task as a constrained optimization problem and consider the resulting ingredient mix as a 'hot' candidate. Starting off with a very basic formulation that merely demands the necessities of our problem to be fulfilled, we incorporate additional desired conditions into the problem formulation and compare the resulting cocktail recipes.
  • Supervised graph summarization for structuring academic search results (Mirylenka and Passerini) [pdf]
    In this paper we address the problem of visualizing the query results of the academic search services. We suggest representing the search results as concise topic hierarchies, and propose a method of building such hierarchies through summarization of the intermediate large topic graphs. We describe a supervised learning technique for summarizing the topic graphs in the most informative way using sequential structured prediction, and discuss our ongoing work on the interactive acquisition of the training examples.
  • Hybrid SRL with Optimization Modulo Theories (Teso, Sebastiani, and Passerini) [pdf]
    Generally speaking, the goal of constructive learning could be seen as, given an example set of structured objects, to generate novel objects with similar properties. From a statistical-relational learning (SRL) viewpoint, the task can be interpreted as a constraint satisfaction problem, i.e. the generated objects must obey a set of soft constraints, whose weights are estimated from the data. Traditional SRL approaches rely on (finite) First-Order Logic (FOL) as a description language, and on MAX-SAT solvers to perform inference. Alas, FOL is unsuited for constructive problems where the objects contain a mixture of Boolean and numerical variables. It is in fact difficult to implement, e.g. linear arithmetic constraints within the language of FOL. In this paper we propose a novel class of hybrid SRL methods that rely on Satisfiability Modulo Theories, an alternative class of formal languages that allow to describe, and reason over, mixed Boolean-numerical objects and constraints. The resulting methods, which we call Learning Modulo Theories, are formulated within the structured output SVM framework, and employ a weighted SMT solver as an optimization oracle to perform efficient inference and discriminative max margin weight learning. We also present a few examples of constructive learning applications enabled by our method.
  1. Varun Aggarwal, Shashank Srikant, and Vinay Shashidhar
    Principles for using Machine Learning in the Assessment of Open Response Items: Programming Assessment as a Case Study
  2. Sumit Basu, Chuck Jacobs and Lucy Vanderwende
    Powergrading: a Clustering Approach to Amplify Human Effort for Short Answer Grading
  3. Franck Dernoncourt, Choung Do, Sherif Halawa, Una-May O’Reilly, Colin Taylor, Kalyan Veeramachaneni and Sherwin Wu
    MOOCVIZ: A Large Scale, Open Access,Collaborative, Data Analytics Platform for MOOCs
  4. Jorge Diez, Oscar Luaces, Amparo Alonso-Betanzos, Alicia Troncoso and Antonio Bahamonde
    Peer Assessment in MOOCs Using Preference Learning via Matrix Factorization
  5. Stephen E. Fancsali
    Data-driven causal modeling of “gaming the system” and off-task behavior in Cognitive Tutor Algebra
  6. Damien Follet
    A three-steps classification algorithm to assist criteria grid assessment
  7. Peter W. Foltz and Mark Rosenstein
    Tracking Student Learning in a State-Wide Implementation of Automated Writing Scoring
  8. Jose P. Gonzalez-Brenes, Yun Huang and Peter Brusilovsky
    FAST: Feature-Aware Student Knowledge Tracing
  9. Fang Han, Kalyan Veeramachaneni and Una-May O’Reilly
    Analyzing student behavior during problem solving in MOOCs
  10. Mohammad Khajah, Rowan M. Wing, Robert V. Lindsey and Michael C. Mozer
    Incorporating Latent Factors Into Knowledge Tracing To Predict Individual Differences In Learning
  11. Robert V. Lindsey, Jeff D. Shroyer, Harold Pashler and Michael C. Mozer
    Improving students’ long-term knowledge retention through personalized review
  12. Yun-En Liu, Travis Mandel, Zoran Popovic and Emma Brunskill
    Towards Automatic Experimentation of Educational Knowledge
  13. Andras Lorincz, Gyongyver Molnar, Laszlo A. Jeni, Zoltan Toser, Attila Rausch and Jeffrey F. Cohn
    Towards entertaining and efficient educational games
  14. Travis Mandel, Yun-En Liu, Zoran Popovic, Sergey Levin and Emma Brunskill
    Unbiased Offline Evaluation of Policy Representations for Educational Games
  15. Sergiy Nesterko, Svetlana Dotsenko, Qiuyi Hu, Daniel Seaton, Justin Reich, Isaac Chuang, and Andrew Ho
    Evaluating Geographic Data in MOOCs
  16. Andy Nguyen, Christopher Piech, Jonathan Huang and Leonidas Guibas
    Codewebs: Scalable Code Search for MOOCs
  17. Zachary A. Pardos
    Simulation study of a HMM based automatic resource recommendation system
  18. Arti Ramesh, Dan Goldwasser, Bert Huang, Snigdha Chaturvedi, Hal Daume III and Lise Getoor
    Modeling Learner Engagement in MOOCs using Probabilistic Soft Logic
  19. Nihar B. Shah, Joseph K. Bradley, Abhay Parekh, Martin Wainwright and Kannan Ramchandran
    A Case for Ordinal Peer Evaluation in MOOCs
  20. Adish Singla, Ilija Bogunovic, Gabor Bartok, Amin Karbasi and Andreas Krause
    On Actively Teaching the Crowd to Classify
  21. Glenda S. Stump, Jennifer DeBoer, Jonathan Whittinghill and Lori Breslow
    Development of a Framework to Classify MOOC Discussion Forum Posts: Methodology and Challenges
  22. Weiyi Sun, Siwei Lyu, Hui Jin and Jianwei Zhang
    Analyzing Online Learning Discourse using Probabilistic Topic Models
  23. Joseph Jay Williams
    Applying Cognitive Science to Online Learning
  24. Joseph Jay Williams and Betsy Williams
    Using Interventions to Improve Online Learning
  25. Diyii Yang, Tanmay Sinha, David Adamson and Carolyn Penstein Rose
    “Turn on, Tune in, Drop out”: Anticipating student dropouts in Massive Open Online Courses

Poster Session I

Yuxin Chen, Hiroaki Shioi, Cesar Antonio Fuentes Montesinos, Lian Pin Koh, Serge Wich, Andreas Krause.
Active Detection for Biodiversity Monitoring via Adaptive Submodularity.

Christopher R. Dance, Stephane Clinchant, Onno R. Zoeter.
Approximate Inference for a Non-Homogeneous Poisson Model of On-Street Parking. [pdf]

George Mathews, John Vial, Sanjeev Jha, Gregoire Mariethoz, Nickens Okello, Suhinthan Maheswararajah, Dom De Re, Michael Smith.
Bayesian Inference of the Hydraulic Properties of Deep Geological Formations.

Simon O’Callaghan, Alistair Reid, Lachlan McCalman, Edwin V. Bonilla, Fabio Ramos
Bayesian Joint Inversions for the Exploration and Characterization of Geothermal Targets. [pdf]

Jun Yu, Weng-Keen Wong, Steve Kelling.
Clustering Species Accumulation Curves to Identify Groups of Citizen Scientists with Similar Skill Levels. [pdf]

Kalyan Veeramachaneni, Teasha Feldman-Fitzthum, Una-May O’Reilly, Alfredo Cuesta-Infante.
Copula-Based Wind Resource Assessment. [pdf]

Danny Panknin, Tammo Krueger, Mikio Braun, Klaus-Robert Muller, Siegmund Duell.
Detecting changes in Wind Turbine Sensory Data. [pdf]

Shan Xue, Alan Fern, Daniel Sheldon.
Dynamic Resource Allocation for Optimizing Population Diffusion.

Nidhi Singh.
Green-Aware Workload Prediction for Non-stationary Environments.

Mingjun Zhong, Nigel Goddard, Charles Sutton.
Interleaved Factorial Non-Homogeneous Hidden Markov Models for Energy Disaggregation. [pdf]


Poster Session II

Tao Sun, Daniel Sheldon, Akshat Kumar.
Message Passing for Collective Graphical Models. [pdf]

Jun Yu, Rebecca A. Hutchinson, Weng-Keen Wong.
Modeling Misidentification of Bird Species by Citizen Scientists. [pdf]

Anna Ogawa, Akiko Takeda, Toru Namerikawa.
Photovoltaic Output Prediction Using Auto-regression with Support Vector Machine. [pdf]

Rebecca A. Hutchinson, Thomas G. Dietterich.
Posterior Regularization for Occupancy Models.

Xiaojian Wu , Daniel Sheldon, Shlomo Zilberstein.
Stochastic Network Design for River Networks. [pdf]

Daniel Urieli, Peter Stone.
TacTex’13- An Adaptive Champion Power Trading Agent.

Bingsheng Wang, Haili Dong, Chang-Tien Lu.
Using Step Variant Convolutional Neural Networks for Energy Disaggregation. [pdf]

Angela Fernandez, Carlos M. Alaiz, Ana M. Gonzalez, Julia Diaz, Jose R. Dorronsoro
Local Anisotropic Diffusion Detection of Wind Ramps. [pdf]

Mahsa Ghafrianzadeh, Claire Monteleoni.
Climate Prediction via Matrix Completion. [pdf]


AFTERNOON SESSION (3:30-6:30)


Domain Adaptation as Learning with Auxiliary Information
Shai Ben-David, Ruth Urner

Sample Complexity of Sequential Multi-task Reinforcement Learning
Emma Brunskill, Lihong Li

Sequential Transfer in Multi-armed Bandit with Logarithmic Transfer Regret
Mohammad Gheshlaghi Azar, Alessandro Lazaric, Emma Brunskill

Class-wise Density-ratios for Covariate Shift
Yun-Qian Miao, Ahmed K. Farahat, Mohamed S. Kamel

Domain adaptation for sequence labeling using hidden Markov models

Edouard Grave, Guillaume Obozinski,  Francis Bach

Retrieval of Experiments: Sequential Dirichlet Process Mixtures in Model Space
Ritabrata Dutta, Sohan Seth, Samuel Kaski

Multitask Learning with Feature Selection for Groups of Related Tasks
Meenakshi Mishra, Jun Huan

Restricted Transfer Learning for Text Categorization
Rajhans Samdani, Gideon Mann

Transform-based Domain Adaptation for Big Data
Erik Rodner, Judy Hoffman, Trevor Darrell, Jeff Donahue, Kate Saenko

A PAC-Bayesian bound for Lifelong Learning
Anastasia Pentina, Christoph H. Lampert

Multi-task Bilinear Classifiers for Visual Domain Adaptation
Jiaolong Xu, Sebastian Ramos, Xu Hu, David Vazquez, Antonio M. Lopez

Tree-Based Ensemble Multi-Task Learning Method for Classification and Regression
Jaak Simm, Ildefons Magrans de Abril, Masashi Sugiyama

Domain Adaptation of Majority Votes via Perturbed Variation-based Label Transfer
Emilie Morvant

Multilinear Spectral Regularization for Kernel-based Multitask Learning
Marco Signoretto, Johan A.K. Suykens
Reinforcement Learning with Multi-Fidelity Simulators

Sameer Singh, Sebastian Riedel, and Andrew McCallum. Anytime belief propagation using sparse domains.


W00085459.jpg was taken on December 02, 2013 and received on Earth December 04, 2013. The camera was pointing toward SATURN at approximately 710,353 miles (1,143,202 kilometers) away, and the image was taken using the MT2 and CL2 filters. This image has not been validated or calibrated. 

Image Credit: NASA/JPL/Space Science Institute


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