OpenRaiser/Intern-Atlas huggingface dataset:
Stereo Matching by Training a Convolutional Neural Network to Compare Image Patches
Venue: Journal JMLR 2016
Year: 2016

We present a method for extracting depth information from a rectified image pair. Our approach focuses on the first stage of many stereo algorithms: the matching cost computation. We approach the problem by learning a similarity measure on small image patches using a convolutional neural network. Training is carried out in a supervised manner by constructing a binary classification data set with examples of similar and dissimilar pairs of patches. We examine two network architectures for this task: one tuned for speed, the other for accuracy. The output of the convolutional neural network is used to initialize the stereo matching cost. A series of post-processing steps follow: cross-based cost aggregation, semiglobal matching, a left-right consistency check, subpixel enhancement, a median filter, and a bilateral filter. We evaluate our method on the KITTI 2012, KITTI 2015, and Middlebury stereo data sets and show that it outperforms other approaches on all three data sets.
True Online Temporal-Difference Learning
Venue: Journal JMLR 2016
Year: 2016

The temporal-difference methods TD($λ$) and Sarsa($λ$) form a core part of modern reinforcement learning. Their appeal comes from their good performance, low computational cost, and their simple interpretation, given by their forward view. Recently, new versions of these methods were introduced, called true online TD($λ$) and true online Sarsa($λ$), respectively (van Seijen & Sutton, 2014). These new versions maintain an exact equivalence with the forward view at all times, whereas the traditional versions only approximate it for small step-sizes. We hypothesize that these true online methods not only have better theoretical properties, but also dominate the regular methods empirically. In this article, we put this hypothesis to the test by performing an extensive empirical comparison. Specifically, we compare the performance of true online TD($λ$)/Sarsa($λ$) with regular TD($λ$)/Sarsa($λ$) on random MRPs, a real-world myoelectric prosthetic arm, and a domain from the Arcade Learning Environment. We use linear function approximation with tabular, binary, and non-binary features. Our results suggest that the true online methods indeed dominate the regular methods. Across all domains/representations the learning speed of the true online methods are often better, but never worse than that of the regular methods. An additional advantage is that no choice between traces has to be made for the true online methods. Besides the empirical results, we provide an in-depth analysis of the theory behind true online temporal-difference learning. In addition, we show that new true online temporal-difference methods can be derived by making changes to the online forward view and then rewriting the update equations.
Refined Error Bounds for Several Learning Algorithms
Venue: Journal JMLR 2016
Year: 2016

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error rates of sample-consistent classifiers with monotonic error regions, in the realizable case. We prove bounds of this type expressed in terms of either the VC dimension or the sample compression size. This general technique also enables us to derive several new bounds on the error rates of general sample-consistent learning algorithms, as well as refined bounds on the label complexity of the CAL active learning algorithm. Additionally, we establish a simple necessary and sufficient condition for the existence of a distribution-free bound on the error rates of all sample-consistent learning rules, converging at a rate inversely proportional to the sample size. We also study learning in the presence of classification noise, deriving a new excess error rate guarantee for general VC classes under Tsybakov's noise condition, and establishing a simple and general necessary and sufficient condition for the minimax excess risk under bounded noise to converge at a rate inversely proportional to the sample size.
Spectral Ranking using Seriation
Venue: Journal JMLR 2016
Year: 2016

We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a similarity matrix from pairwise comparisons, using seriation methods to reorder this matrix and construct a ranking. We first show that this spectral seriation algorithm recovers the true ranking when all pairwise comparisons are observed and consistent with a total order. We then show that ranking reconstruction is still exact when some pairwise comparisons are corrupted or missing, and that seriation based spectral ranking is more robust to noise than classical scoring methods. Finally, we bound the ranking error when only a random subset of the comparions are observed. An additional benefit of the seriation formulation is that it allows us to solve semi-supervised ranking problems. Experiments on both synthetic and real datasets demonstrate that seriation based spectral ranking achieves competitive and in some cases superior performance compared to classical ranking methods.
Local Network Community Detection with Continuous Optimization of Conductance and Weighted Kernel K-Means
Venue: Journal JMLR 2016
Year: 2016

Local network community detection is the task of finding a single community of nodes concentrated around few given seed nodes in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. This paper studies a continuous relaxation of conductance. We show that continuous optimization of this objective still leads to discrete communities. We investigate the relation of conductance with weighted kernel k-means for a single community, which leads to the introduction of a new objective function, $σ$-conductance. Conductance is obtained by setting $σ$ to $0$. Two algorithms, EMc and PGDc, are proposed to locally optimize $σ$-conductance and automatically tune the parameter $σ$. They are based on expectation maximization and projected gradient descent, respectively. We prove locality and give performance guarantees for EMc and PGDc for a class of dense and well separated communities centered around the seeds. Experiments are conducted on networks with ground-truth communities, comparing to state-of-the-art graph diffusion algorithms for conductance optimization. On large graphs, results indicate that EMc and PGDc stay localized and produce communities most similar to the ground, while graph diffusion algorithms generate large communities of lower quality.
The Asymptotic Performance of Linear Echo State Neural Networks
Venue: Journal JMLR 2016
Year: 2016

In this article, a study of the mean-square error (MSE) performance of linear echo-state neural networks is performed, both for training and testing tasks. Considering the realistic setting of noise present at the network nodes, we derive deterministic equivalents for the aforementioned MSE in the limit where the number of input data $T$ and network size $n$ both grow large. Specializing then the network connectivity matrix to specific random settings, we further obtain simple formulas that provide new insights on the performance of such networks.
Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation
Venue: Journal JMLR 2016
Year: 2016

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable manifold. While many optimization problems are of the described form, technicalities of differential geometry and the laborious calculation of derivatives pose a significant barrier for experimenting with these methods. We introduce Pymanopt (available at https://pymanopt.github.io), a toolbox for optimization on manifolds, implemented in Python, that---similarly to the Manopt Matlab toolbox---implements several manifold geometries and optimization algorithms. Moreover, we lower the barriers to users further by using automated differentiation for calculating derivative information, saving users time and saving them from potential calculation and implementation errors.
Neural Autoregressive Distribution Estimation
Venue: Journal JMLR 2016
Year: 2016

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.
Scalable Influence Maximization for Multiple Products in Continuous-Time Diffusion Networks
Venue: Journal JMLR 2017
Year: 2017

A typical viral marketing model identifies influential users in a social network to maximize a single product adoption assuming unlimited user attention, campaign budgets, and time. In reality, multiple products need campaigns, users have limited attention, convincing users incurs costs, and advertisers have limited budgets and expect the adoptions to be maximized soon. Facing these user, monetary, and timing constraints, we formulate the problem as a submodular maximization task in a continuous-time diffusion model under the intersection of a matroid and multiple knapsack constraints. We propose a randomized algorithm estimating the user influence in a network ($|\mathcal{V}|$ nodes, $|\mathcal{E}|$ edges) to an accuracy of $ε$ with $n=\mathcal{O}(1/ε^2)$ randomizations and $\tilde{\mathcal{O}}(n|\mathcal{E}|+n|\mathcal{V}|)$ computations. By exploiting the influence estimation algorithm as a subroutine, we develop an adaptive threshold greedy algorithm achieving an approximation factor $k_a/(2+2 k)$ of the optimal when $k_a$ out of the $k$ knapsack constraints are active. Extensive experiments on networks of millions of nodes demonstrate that the proposed algorithms achieve the state-of-the-art in terms of effectiveness and scalability.
Hierarchically Compositional Kernels for Scalable Nonparametric Learning
Venue: Journal JMLR 2017
Year: 2017

We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where the Nyström method (a globally low-rank approximation) is married with a locally lossless approximation in a hierarchical fashion. The kernel maintains (strict) positive-definiteness. The corresponding kernel matrix admits a recursively off-diagonal low-rank structure, which allows for fast linear algebra computations. Suppressing the factor of data dimension, the memory and arithmetic complexities for training a regression or a classifier are reduced from $O(n^2)$ and $O(n^3)$ to $O(nr)$ and $O(nr^2)$, respectively, where $n$ is the number of training examples and $r$ is the rank on each level of the hierarchy. Although other randomized approximate kernels entail a similar complexity, empirical results show that the proposed kernel achieves a matching performance with a smaller $r$. We demonstrate comprehensive experiments to show the effective use of the proposed kernel on data sizes up to the order of millions.
SnapVX: A Network-Based Convex Optimization Solver
Venue: Journal JMLR 2017
Year: 2017

SnapVX is a high-performance Python solver for convex optimization problems defined on networks. For these problems, it provides a fast and scalable solution with guaranteed global convergence. SnapVX combines the capabilities of two open source software packages: Snap.py and CVXPY. Snap.py is a large scale graph processing library, and CVXPY provides a general modeling framework for small-scale subproblems. SnapVX offers a customizable yet easy-to-use interface with out-of-the-box functionality. Based on the Alternating Direction Method of Multipliers (ADMM), it is able to efficiently store, analyze, and solve large optimization problems from a variety of different applications. Documentation, examples, and more can be found on the SnapVX website at http://snap.stanford.edu/snapvx.
On the Consistency of Ordinal Regression Methods
Venue: Journal JMLR 2017
Year: 2017

Many of the ordinal regression models that have been proposed in the literature can be seen as methods that minimize a convex surrogate of the zero-one, absolute, or squared loss functions. A key property that allows to study the statistical implications of such approximations is that of Fisher consistency. Fisher consistency is a desirable property for surrogate loss functions and implies that in the population setting, i.e., if the probability distribution that generates the data were available, then optimization of the surrogate would yield the best possible model. In this paper we will characterize the Fisher consistency of a rich family of surrogate loss functions used in the context of ordinal regression, including support vector ordinal regression, ORBoosting and least absolute deviation. We will see that, for a family of surrogate loss functions that subsumes support vector ordinal regression and ORBoosting, consistency can be fully characterized by the derivative of a real-valued function at zero, as happens for convex margin-based surrogates in binary classification. We also derive excess risk bounds for a surrogate of the absolute error that generalize existing risk bounds for binary classification. Finally, our analysis suggests a novel surrogate of the squared error loss. We compare this novel surrogate with competing approaches on 9 different datasets. Our method shows to be highly competitive in practice, outperforming the least squares loss on 7 out of 9 datasets.
Distributed Learning with Regularized Least Squares
Venue: Journal JMLR 2017
Year: 2017

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, and then takes an average of the individual output functions as a final global estimator or predictor. We show with error bounds in expectation in both the $L^2$-metric and RKHS-metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine. Our error bounds are sharp and stated in a general setting without any eigenfunction assumption. The analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach. Even for the classical least squares regularization scheme in the RKHS associated with a general kernel, we give the best learning rate in the literature.
Hinge-Loss Markov Random Fields and Probabilistic Soft Logic
Venue: Journal JMLR 2017
Year: 2017

A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible.
Risk-Constrained Reinforcement Learning with Percentile Risk Criteria
Venue: Journal JMLR 2017
Year: 2017

In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we first derive a formula for computing the gradient of the Lagrangian function for percentile risk-constrained MDPs. Then, we devise policy gradient and actor-critic algorithms that (1) estimate such gradient, (2) update the policy in the descent direction, and (3) update the Lagrange multiplier in the ascent direction. For these algorithms we prove convergence to locally optimal policies. Finally, we demonstrate the effectiveness of our algorithms in an optimal stopping problem and an online marketing application.
Optimal Dictionary for Least Squares Representation
Venue: Journal JMLR 2017
Year: 2017

Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., $\ell_0$-optimal representations. Here we consider the problem of finding optimal dictionaries with which representations of samples of a random vector are optimal in an $\ell_2$-sense: optimality of representation is defined as attaining the minimal average $\ell_2$-norm of the coefficients used to represent the random vector. With the help of recent results on rank-$1$ decompositions of symmetric positive semidefinite matrices, we provide an explicit description of $\ell_2$-optimal dictionaries as well as their algorithmic constructions in polynomial time.
Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques
Venue: Journal JMLR 2017
Year: 2017

In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on partitioning weighted uniform hypergraphs---a problem often encountered in computer vision. This work is motivated by two issues that arise when a hypergraph partitioning approach is used to tackle computer vision problems: (i) The uniform hypergraphs constructed for higher-order learning contain all edges, but most have negligible weights. Thus, the adjacency tensor is nearly sparse, and yet, not binary. (ii) A more serious concern is that standard partitioning algorithms need to compute all edge weights, which is computationally expensive for hypergraphs. This is usually resolved in practice by merging the clustering algorithm with a tensor sampling strategy---an approach that is yet to be analysed rigorously. We build on our earlier work on partitioning dense unweighted uniform hypergraphs (Ghoshdastidar and Dukkipati, ICML, 2015), and address the aforementioned issues by proposing provable and efficient partitioning algorithms. Our analysis justifies the empirical success of practical sampling techniques. We also complement our theoretical findings by elaborate empirical comparison of various hypergraph partitioning schemes.
Multiscale Strategies for Computing Optimal Transport
Venue: Journal JMLR 2017
Year: 2017

This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically low-dimensional. The approach is based on an adaptive multiscale decomposition of the point sets. The multiscale decomposition yields a sequence of optimal transport problems, that are solved in a top-to-bottom fashion from the coarsest to the finest scale. We provide numerical evidence that this multiscale approach scales approximately linearly, in time and memory, in the number of nodes, instead of quadratically or worse for a direct solution. Empirically, the multiscale approach results in less than one percent relative error in the objective function. Furthermore, the multiscale plans constructed are of interest by themselves as they may be used to introduce novel features and notions of distances between point sets. An analysis of sets of brain MRI based on optimal transport distances illustrates the effectiveness of the proposed method on a real world data set. The application demonstrates that multiscale optimal transport distances have the potential to improve on state-of-the-art metrics currently used in computational anatomy.
Approximation Vector Machines for Large-scale Online Learning
Venue: Journal JMLR 2017
Year: 2017

One of the most challenging problems in kernel online learning is to bound the model size and to promote the model sparsity. Sparse models not only improve computation and memory usage, but also enhance the generalization capacity, a principle that concurs with the law of parsimony. However, inappropriate sparsity modeling may also significantly degrade the performance. In this paper, we propose Approximation Vector Machine (AVM), a model that can simultaneously encourage the sparsity and safeguard its risk in compromising the performance. When an incoming instance arrives, we approximate this instance by one of its neighbors whose distance to it is less than a predefined threshold. Our key intuition is that since the newly seen instance is expressed by its nearby neighbor the optimal performance can be analytically formulated and maintained. We develop theoretical foundations to support this intuition and further establish an analysis to characterize the gap between the approximation and optimal solutions. This gap crucially depends on the frequency of approximation and the predefined threshold. We perform the convergence analysis for a wide spectrum of loss functions including Hinge, smooth Hinge, and Logistic for classification task, and $l_1$, $l_2$, and $ε$-insensitive for regression task. We conducted extensive experiments for classification task in batch and online modes, and regression task in online mode over several benchmark datasets. The results show that our proposed AVM achieved a comparable predictive performance with current state-of-the-art methods while simultaneously achieving significant computational speed-up due to the ability of the proposed AVM in maintaining the model size.