Learning the dependency structure between spatially distributed observations of a spatio-temporal process is an important problem in many fields such as geology, geophysics, atmospheric sciences, oceanography, etc. . However, estimation of such systems is complicated by the fact that they exhibit dynamics at multiple scales of space and time arising due to a combination of diffusion and convection/advection. As we show, time-series graphical models based on vector auto-regressive processes are inefficient in capturing such multi-scale structure. In this paper, we present a hierarchical graphical model with physically derived priors that better represents the multi-scale character of these dynamical systems. We also propose algorithms to efficiently estimate the interaction structure from data. We demonstrate results on a general class of problems arising in exploration geophysics by discovering graphical structure that is physically meaningful and provide evidence of its advantages over alternative approaches.

We extend generative stochastic networks to supervised learning of representations. In particular, we introduce a hybrid training objective considering a generative and discriminative cost function governed by a trade-off parameter lambda. We use a new variant of network training involving noise injection, i.e. walkback training, to jointly optimize multiple network layers. Neither additional regularization constraints, such as l1, l2 norms or dropout variants, nor pooling- or convolutional layers were added. Nevertheless, we are able to obtain state-of-the-art performance on the MNIST dataset, without using permutation invariant digits and outperform baseline models on sub-variants of the MNIST and rectangles dataset significantly.

We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. It shows competitive performance on standard benchmark datasetsagainst a number of other representative algorithms in the literature. We also discuss extensions of RoBiRank to large scale problems where explicit feature vectors and scores are not given. We show that RoBiRank can be efficiently parallelizedacross a large number of machines; for a task that requires 386, 133 49, 824, 519 pairwise interactions between items to be ranked, RoBi-Rank finds solutions that are of dramatically higher quality than that can be found by a state-of-the-art competitor algorithm, given the same amount of wall-clock time for computation.

Distributed machine learning has typically been approached from a data parallel perspective, where big data are partitioned to multiple workers and an algorithm is executed concurrently over different data subsets under various synchronization schemes to ensure speed-up and/or correctness. A sibling problem that has received relatively less attention is how to ensure efficient and correct model parallel execution of ML algorithms, where parameters of an ML program are partitioned to different workers and undergone concurrent iterative updates. We argue that model and data parallelisms impose rather different challenges for system design, algorithmic adjustment, and theoretical analysis. In this paper, we develop a system for model-parallelism, STRADS, that provides a programming abstraction for scheduling parameter updates by discovering and leveraging changing structural properties of ML programs. STRADS enables a flexible tradeoff between scheduling efficiency and fidelity to intrinsic dependencies within the models, and improves memory efficiency of distributed ML. We demonstrate the efficacy of model-parallel algorithms implemented on STRADS versus popular implementations for topic modeling, matrix factorization, and Lasso.

Motivated by generating personalized recommendations using ordinal (or preference) data, we study the question of learning a mixture of MultiNomial Logit (MNL) model, a parameterized class of distributions over permutations, from partial ordinal or preference data (e.g. pair-wise comparisons). Despite its long standing importance across disciplines including social choice, operations research and revenue management, little is known about this question. In case of single MNL models (no mixture), computationally and statistically tractable learning from pair-wise comparisons is feasible. However, even learning mixture of two MNL model is infeasible in general. Given this state of affairs, we seek conditions under which it is feasible to learn the mixture model in both computationally and statistically efficient manner. To that end, we present a sufficient condition as well as an efficient algorithm for learning mixed MNL models from partial preferences/comparisons data. In particular, a mixture of $r$ MNL components over $n$ objects can be learnt using samples whose size scales polynomially in $n$ and $r$ (concretely, $n^3 r^{3.5} \log^4 n$, with $r \ll n^{2/7}$ when the model parameters are sufficiently {\em incoherent}). The algorithm has two phases: first, learn the pair-wise marginals for each component using tensor decomposition; second, learn the model parameters for each component using RankCentrality introduced by Negahban et al. In the process of proving these results, we obtain a generalization of existing analysis for tensor decomposition to a more realistic regime where only partial information about each sample is available.

We develop a sampling technique for Hierarchical Dirichlet process models. The parallel algorithm builds upon [Chang & Fisher 2013] by proposing large split and merge moves based on learned sub-clusters. The additional global split and merge moves drastically improve convergence in the experimental results. Furthermore, we discover that cross-validation techniques do not adequately determine convergence, and that previous sampling methods converge slower than were previously expected.

Computing the $k$ dominant eigenvalues and eigenvectors of massive graphs is a key operation in numerous machine learning applications; however, popular solvers suffer from slow convergence, especially when $k$ is reasonably large. In this paper, we propose and analyze a novel multi-scale spectral decomposition method (MSEIGS), which first clusters the graph into smaller clusters whose spectral decomposition can be computed efficiently and independently. We show theoretically as well as empirically that the union of all cluster's subspaces has significant overlap with the dominant subspace of the original graph, provided that the graph is clustered appropriately. Thus, eigenvectors of the clusters serve as good initializations to a block Lanczos algorithm that is used to compute spectral decomposition of the original graph. We further use hierarchical clustering to speed up the computation and adopt a fast early termination strategy to compute quality approximations. Our method outperforms widely used solvers in terms of convergence speed and approximation quality. Furthermore, our method is naturally parallelizable and exhibits significant speedups in shared-memory parallel settings. For example, on a graph with more than 82 million nodes and 3.6 billion edges, MSEIGS takes less than 3 hours on a single-core machine while Randomized SVD takes more than 6 hours, to obtain a similar approximation of the top-50 eigenvectors. Using 16 cores, we can reduce this time to less than 40 minutes.

The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in general difficult, and developing Gaussian process models for this purpose involves several challenges. A vast majority of kernels, and kernel learning methods, currently only succeed in smoothing and interpolation. This difficulty is compounded by the fact that Gaussian processes are typically only tractable for small datasets, and scaling an expressive kernel learning approach poses different challenges than scaling a standard Gaussian process model. One faces additional computational constraints, and the need to retain significant model structure for expressing the rich information available in a large dataset. In this paper, we propose a Gaussian process approach for large scale multidimensional pattern extrapolation. We recover sophisticated out of class kernels, perform texture extrapolation, inpainting, and video extrapolation, and long range forecasting of land surface temperatures, all on large multidimensional datasets, including a problem with 383,400 training points. The proposed method significantly outperforms alternative scalable and flexible Gaussian process methods, in speed and accuracy. Moreover, we show that a distinct combination of expressive kernels, a fully non-parametric representation, and scalable inference which exploits existing model structure, are critical for large scale multidimensional pattern extrapolation.

Stochastic variational inference (SVI) lets us scale up Bayesian computation to massive data. It uses stochastic optimization to fit a variational distribution, following easy-to-computenoisy natural gradients. As with most traditional stochastic optimization methods, SVI takes precautions to use unbiased stochastic gradients whoseexpectations are equal to the true gradients. In this paper, we explore the idea of following biased stochastic gradients in SVI. Our method replaces the natural gradient with a similarly constructed vector that uses a fixed-window moving average of some of its previous terms. We will demonstrate the many advantages ofthis technique. First, its computational cost is the same as for SVI and storage requirements only multiply by a constant factor. Second, it enjoys significant variancereduction over the unbiased estimates, smaller bias than averaged gradients, and leads to smaller mean-squared error against the full gradient. We test our method on latent Dirichlet allocation with three large corpora.

Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost. In this paper, we present two novel insights for improving the prediction efficiency of kernel machines. First, we show that by adding “pseudo landmark points” to the classical Nystr¨om kernel approximation in an elegant way, we can significantly reduce the prediction error without much additional prediction cost. Second, we provide a new theoretical analysis on bounding the error of the solution computed by using Nystr¨om kernel approximation method, and show that the error is related to the weighted kmeans objective function where the weights are given by the model computed from the original kernel. This theoretical insight suggests a new landmark point selection technique for the situation where we have knowledge of the original model. Based on these two insights, we provide a divide-and-conquer framework for improving the prediction speed. First, we divide the whole problem into smaller local subproblems to reduce the problem size. In the second phase, we develop a kernel approximation based fast prediction approach within each subproblem. We apply our algorithm to real world large-scale classification and regression datasets, and show that the proposed algorithm is consistently and significantly better than other competitors. For example, on the Covertype classification problem, in terms of prediction time, our algorithm achieves more than 10000 times speedup over the full kernel SVM, and a two-fold speedup over the state-of-the-art LDKL approach, while obtaining much higher prediction accuracy than LDKL (95.2% vs. 89.53%).