OpenRaiser/Intern-Atlas huggingface dataset:
Nonnegative matrix factorization via rank-one downdate
Venue: Conference ICML 2008
Year: 2008

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries. We propose an algorithm called rank-one downdate (R1D) for computing a NMF that is partly motivated by singular value decomposition. This algorithm computes the dominant singular values and vectors of adaptively determined submatrices of a matrix. On each iteration, R1D extracts a rank-one submatrix from the dataset according to an objective function. We establish a theoretical result that maximizing this objective function corresponds to correctly classifying articles in a nearly separable corpus. We also provide computational experiments showing the success of this method in identifying features in realistic datasets.
Prediction with expert advice for the Brier game
Venue: Conference ICML 2008
Year: 2008

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical performance guarantee turns out to be rather tight on these data sets, especially in the case of the more extensive tennis data.
Multi-instance learning by treating instances as non-I.I.D. samples
Venue: Conference ICML 2009
Year: 2009

Multi-instance learning attempts to learn from a training set consisting of labeled bags each containing many unlabeled instances. Previous studies typically treat the instances in the bags as independently and identically distributed. However, the instances in a bag are rarely independent, and therefore a better performance can be expected if the instances are treated in an non-i.i.d. way that exploits the relations among instances. In this paper, we propose a simple yet effective multi-instance learning method, which regards each bag as a graph and uses a specific kernel to distinguish the graphs by considering the features of the nodes as well as the features of the edges that convey some relations among instances. The effectiveness of the proposed method is validated by experiments.
Efficient Learning with Partially Observed Attributes
Venue: Conference ICML 2010
Year: 2010

We describe and analyze efficient algorithms for learning a linear predictor from examples when the learner can only view a few attributes of each training example. This is the case, for instance, in medical research, where each patient participating in the experiment is only willing to go through a small number of tests. Our analysis bounds the number of additional examples sufficient to compensate for the lack of full information on each training example. We demonstrate the efficiency of our algorithms by showing that when running on digit recognition data, they obtain a high prediction accuracy even when the learner gets to see only four pixels of each image.
Asymptotic Analysis of Generative Semi-Supervised Learning
Venue: Conference ICML 2010
Year: 2010

Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP.
Interactive Submodular Set Cover
Venue: Conference ICML 2010
Year: 2010

We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation guarantee for a novel greedy algorithm and give a hardness of approximation result which matches up to constant factors. We also discuss negative results for simpler approaches and present encouraging early experimental results.
Feature Selection Using Regularization in Approximate Linear Programs for Markov Decision Processes
Venue: Conference ICML 2010
Year: 2010

Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. We address this shortcoming using $L_1$ regularization in approximate linear programming. Because the proposed method can automatically select the appropriate richness of features, its performance does not degrade with an increasing number of features. These results rely on new and stronger sampling bounds for regularized approximate linear programs. We also propose a computationally efficient homotopy method. The empirical evaluation of the approach shows that the proposed method performs well on simple MDPs and standard benchmark problems.
Should one compute the Temporal Difference fix point or minimize the Bellman Residual? The unified oblique projection view
Venue: Conference ICML 2010
Year: 2010

We investigate projection methods, for evaluating a linear approximation of the value function of a policy in a Markov Decision Process context. We consider two popular approaches, the one-step Temporal Difference fix-point computation (TD(0)) and the Bellman Residual (BR) minimization. We describe examples, where each method outperforms the other. We highlight a simple relation between the objective function they minimize, and show that while BR enjoys a performance guarantee, TD(0) does not in general. We then propose a unified view in terms of oblique projections of the Bellman equation, which substantially simplifies and extends the characterization of (schoknecht,2002) and the recent analysis of (Yu & Bertsekas, 2008). Eventually, we describe some simulations that suggest that if the TD(0) solution is usually slightly better than the BR solution, its inherent numerical instability makes it very bad in some cases, and thus worse on average.
Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
Venue: Conference ICML 2010
Year: 2010

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches.
Parallel Coordinate Descent for L1-Regularized Loss Minimization
Venue: Conference ICML 2011
Year: 2011

We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1-regularized losses. Though coordinate descent seems inherently sequential, we prove convergence bounds for Shotgun which predict linear speedups, up to a problem-dependent limit. We present a comprehensive empirical study of Shotgun for Lasso and sparse logistic regression. Our theoretical predictions on the potential for parallelism closely match behavior on real data. Shotgun outperforms other published solvers on a range of large problems, proving to be one of the most scalable algorithms for L1.
Doubly Robust Policy Evaluation and Learning
Venue: Conference ICML 2011
Year: 2011

We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strength and overcome the weaknesses of the two approaches by applying the doubly robust technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust approach uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice.
Uncovering the Temporal Dynamics of Diffusion Networks
Venue: Conference ICML 2011
Year: 2011

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission rates between nodes and transmission sources are unknown. Inferring the underlying dynamics is of outstanding interest since it enables forecasting, influencing and retarding infections, broadly construed. To this end, we model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Given cascade data -- observed infection times of nodes -- we infer the edges of the global diffusion network and estimate the transmission rates of each edge that best explain the observed data. The optimization problem is convex. The model naturally (without heuristics) imposes sparse solutions and requires no parameter tuning. The problem decouples into a collection of independent smaller problems, thus scaling easily to networks on the order of hundreds of thousands of nodes. Experiments on real and synthetic data show that our algorithm both recovers the edges of diffusion networks and accurately estimates their transmission rates from cascade data.
Learning from Multiple Outlooks
Venue: Conference ICML 2011
Year: 2011

We propose a novel problem formulation of learning a single task when the data are provided in different feature spaces. Each such space is called an outlook, and is assumed to contain both labeled and unlabeled data. The objective is to take advantage of the data from all the outlooks to better classify each of the outlooks. We devise an algorithm that computes optimal affine mappings from different outlooks to a target outlook by matching moments of the empirical distributions. We further derive a probabilistic interpretation of the resulting algorithm and a sample complexity bound indicating how many samples are needed to adequately find the mapping. We report the results of extensive experiments on activity recognition tasks that show the value of the proposed approach in boosting performance.
Suboptimal Solution Path Algorithm for Support Vector Machine
Venue: Conference ICML 2011
Year: 2011

We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions provided by this algorithm are very accurate and they satisfy the optimality conditions more strictly than other SVM optimization algorithms. In many machine learning application, however, this strict optimality is often unnecessary, and it adversely affects the computational efficiency. Our algorithm can generate the path of suboptimal solutions within an arbitrary user-specified tolerance level. It allows us to control the trade-off between the accuracy of the solution and the computational cost. Moreover, We also show that our suboptimal solutions can be interpreted as the solution of a \emph{perturbed optimization problem} from the original one. We provide some theoretical analyses of our algorithm based on this novel interpretation. The experimental results also demonstrate the effectiveness of our algorithm.
Implementing regularization implicitly via approximate eigenvector computation
Venue: Conference ICML 2011
Year: 2011

Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective function. This procedure often leads to optimization problems that are computationally more expensive than the original problem, a fact that is clearly problematic if one is interested in large-scale applications. On the other hand, a large body of empirical work has demonstrated that heuristics, and in some cases approximation algorithms, developed to speed up computations sometimes have the side-effect of performing regularization implicitly. Thus, we consider the question: What is the regularized optimization objective that an approximation algorithm is exactly optimizing? We address this question in the context of computing approximations to the smallest nontrivial eigenvector of a graph Laplacian; and we consider three random-walk-based procedures: one based on the heat kernel of the graph, one based on computing the the PageRank vector associated with the graph, and one based on a truncated lazy random walk. In each case, we provide a precise characterization of the manner in which the approximation method can be viewed as implicitly computing the exact solution to a regularized problem. Interestingly, the regularization is not on the usual vector form of the optimization problem, but instead it is on a related semidefinite program.
Mean-Variance Optimization in Markov Decision Processes
Venue: Conference ICML 2011
Year: 2011

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudopolynomial exact and approximation algorithms.
Large-Scale Convex Minimization with a Low-Rank Constraint
Venue: Conference ICML 2011
Year: 2011

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left and right singular vectors corresponding to the largest singular value of a certain matrix, which can be calculated in linear time. This leads to an algorithm which can scale to large matrices arising in several applications such as matrix completion for collaborative filtering and robust low rank matrix approximation.
Minimum Probability Flow Learning
Venue: Conference ICML 2011
Year: 2011

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the KL divergence between the data distribution and the distribution produced by running the dynamics for an infinitesimal time. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate parameter estimation in Ising models, deep belief networks and an independent component analysis model of natural scenes. In the Ising model case, current state of the art techniques are outperformed by at least an order of magnitude in learning time, with lower error in recovered coupling parameters.
Adaptively Learning the Crowd Kernel
Venue: Conference ICML 2011
Year: 2011

We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form "is object 'a' more similar to 'b' or to 'c'?" and is chosen to be maximally informative given the preceding responses. The output is an embedding of the objects into Euclidean space (like MDS); we refer to this as the "crowd kernel." SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as "is striped" among neckties and "vowel vs. consonant" among letters.
Computational Rationalization: The Inverse Equilibrium Problem
Venue: Conference ICML 2011
Year: 2011

Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior is an approximately optimal solution to an unknown decision problem. These techniques learn a utility function that explains the example behavior and can then be used to accurately predict or imitate future behavior in similar observed or unobserved situations. In this work, we consider similar tasks in competitive and cooperative multi-agent domains. Here, unlike single-agent settings, a player cannot myopically maximize its reward --- it must speculate on how the other agents may act to influence the game's outcome. Employing the game-theoretic notion of regret and the principle of maximum entropy, we introduce a technique for predicting and generalizing behavior, as well as recovering a reward function in these domains.
Latent Multi-group Membership Graph Model
Venue: Conference ICML 2012
Year: 2012

We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize the network structure, to predict links between the nodes, and to predict missing features of a node. We derive efficient inference and learning algorithms and evaluate the predictive performance of the LMMG on several social and document network datasets.
Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
Venue: Conference ICML 2012
Year: 2012

In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solve this, but its mixing rate was slow. By leveraging the Bayesian Central Limit Theorem, we extend the SGLD algorithm so that at high mixing rates it will sample from a normal approximation of the posterior, while for slow mixing rates it will mimic the behavior of SGLD with a pre-conditioner matrix. As a bonus, the proposed algorithm is reminiscent of Fisher scoring (with stochastic gradients) and as such an efficient optimizer during burn-in.
Shortest path distance in random k-nearest neighbor graphs
Venue: Conference ICML 2012
Year: 2012

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.
Near-Optimal BRL using Optimistic Local Transitions
Venue: Conference ICML 2012
Year: 2012

Model-based Bayesian Reinforcement Learning (BRL) allows a found formalization of the problem of acting optimally while facing an unknown environment, i.e., avoiding the exploration-exploitation dilemma. However, algorithms explicitly addressing BRL suffer from such a combinatorial explosion that a large body of work relies on heuristic algorithms. This paper introduces BOLT, a simple and (almost) deterministic heuristic algorithm for BRL which is optimistic about the transition function. We analyze BOLT's sample complexity, and show that under certain parameters, the algorithm is near-optimal in the Bayesian sense with high probability. Then, experimental results highlight the key differences of this method compared to previous work.
Decoupling Exploration and Exploitation in Multi-Armed Bandits
Venue: Conference ICML 2012
Year: 2012

We consider a multi-armed bandit problem where the decision maker can explore and exploit different arms at every round. The exploited arm adds to the decision maker's cumulative reward (without necessarily observing the reward) while the explored arm reveals its value. We devise algorithms for this setup and show that the dependence on the number of arms, k, can be much better than the standard square root of k dependence, depending on the behavior of the arms' reward sequences. For the important case of piecewise stationary stochastic bandits, we show a significant improvement over existing algorithms. Our algorithms are based on a non-uniform sampling policy, which we show is essential to the success of any algorithm in the adversarial setup. Finally, we show some simulation results on an ultra-wide band channel selection inspired setting indicating the applicability of our algorithms.
Efficient and Practical Stochastic Subgradient Descent for Nuclear Norm Regularization
Venue: Conference ICML 2012
Year: 2012

We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and parallelizable dense linear algebra operations on small matrices. Our practical algorithms always maintain a low-rank factorization of iterates that can be conveniently held in memory and efficiently multiplied to generate predictions in matrix completion settings. Empirical comparisons confirm that our approach is highly competitive with several recently proposed state-of-the-art solvers for such problems.