ICML 2017 Papers

Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world applications. However, for large-scale problems involving a huge number of samples and extremely high-dimensional features, solving sparse SVMs remains challenging. By noting that sparse SVMs induce sparsities in both feature and sample spaces, we propose a novel approach, which is based on accurate estimations of the primal and dual optima of sparse SVMs, to simultaneously identify the features and samples that are guaranteed to be irrelevant to the outputs. Thus, we can remove the identified inactive samples and features from the training phase, leading to substantial savings in both the memory usage and computational cost without sacrificing accuracy. To the best of our knowledge, the proposed method is the

This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across the data instances. This enables efficient training using stochastic gradients and mini-batches. When this type of training is used, the computational cost does not depend on the number of data instances N. Furthermore, extra assumptions in the approximate inference process make the memory cost independent of N. The consequence is that the proposed EP method can be used on datasets with millions of instances. We compare empirically this method with alternative approaches that approximate the required computations using variational inference. The results show that it performs similar or even better than these techniques, which sometimes give significantly worse predictive distributions in terms of the test log-likelihood. Besides this, the training process of the proposed approach also seems to converge in a smaller number of iterations.

We present a scalable, generative framework for multi-label learning with missing labels. Our framework consists of a latent factor model for the binary label matrix, which is coupled with an exposure model to account for label missingness (i.e., whether a zero in the label matrix is indeed a zero or denotes a missing observation). The underlying latent factor model also assumes that the low-dimensional embeddings of each label vector are directly conditioned on the respective feature vector of that example. Our generative framework admits a simple inference procedure, such that the parameter estimation reduces to a sequence of simple weighted least-square regression problems, each of which can be solved easily, efficiently, and in parallel. Moreover, inference can also be performed in an online fashion using mini-batches of training examples, which makes our framework scalable for large data sets, even when using moderate computational resources. We report both quantitative and qualitative results for our framework on several benchmark data sets, comparing it with a number of state-of-the-art methods.

We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we aim to fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees. In many cases, the computational time is practical and often less than that of decision trees.

In this work we study the safe sequential decision making problem under the setting of adversarial contextual bandits with sequential risk constraints. At each round, nature prepares a context, a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and receives the corresponding cost and risk associated with the pulled arm. In addition to minimizing the cumulative cost, for safety purposes, the learner needs to make safe decisions such that the average of the cumulative risk from all pulled arms should not be larger than a pre-defined threshold. To address this problem, we first study online convex programming in the full information setting where in each round the learner receives an adversarial convex loss and a convex constraint. We develop a meta algorithm leveraging online mirror descent for the full information setting and then extend it to contextual bandit with sequential risk constraints setting using expert advice. Our algorithms can achieve near-optimal regret in terms of minimizing the total cost, while successfully maintaining a sub-linear growth of accumulative risk constraint violation. We support our theoretical results by demonstrating our algorithm on a simple simulated robotics reactive control task.

We present a novel probabilistic framework for a hierarchical extension of independent component analysis (ICA), with a particular motivation in neuroscientific data analysis and modeling. The framework incorporates a general subspace pooling with linear ICA-like layers stacked recursively. Unlike related previous models, our generative model is fully tractable: both the likelihood and the posterior estimates of latent variables can readily be computed with analytically simple formulae. The model is particularly simple in the case of complex-valued data since the pooling can be reduced to taking the modulus of complex numbers. Experiments on electroencephalography (EEG) and natural images demonstrate the validity of the method.

In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic methods such as SVRG, S2GD, SAG and SAGA, SARAH admits a simple recursive framework for updating stochastic gradient estimates; when comparing to SAG/SAGA, SARAH does not require a storage of past gradients. The linear convergence rate of SARAH is proven under strong convexity assumption. We also prove a linear convergence rate (in the strongly convex case) for an inner loop of SARAH, the property that SVRG does not possess. Numerical experiments demonstrate the efficiency of our algorithm.

We describe a learning procedure enhancing L1-penalized regression by adding dynamically generated rules describing multidimensional “box” sets. Our rule-adding procedure is based on the classical column generation method for high-dimensional linear programming. The pricing problem for our column generation procedure reduces to the NP-hard rectangular maximum agreement (RMA) problem of finding a box that best discriminates between two weighted datasets. We solve this problem exactly using a parallel branch-and-bound procedure. The resulting rule-enhanced regression procedure is computation-intensive, but has promising prediction performance.

The problem of automatically generating a computer program from some specification has been studied since the early days of AI. Recently, two competing approaches for `automatic program learning’ have received significant attention: (1) `neural program synthesis’, where a neural network is conditioned on input/output (I/O) examples and learns to generate a program, and (2) `neural program induction’, where a neural network generates new outputs directly using a latent program representation. Here, for the first time, we directly compare both approaches on a large-scale, real-world learning task and we additionally contrast to rule-based program synthesis, which uses hand-crafted semantics to guide the program generation. Our neural models use a modified attention RNN to allow encoding of variable-sized sets of I/O pairs, which achieve 92\% accuracy on a real-world test set, compared to the 34\% accuracy of the previous best neural synthesis approach. The synthesis model also outperforms a comparable induction model on this task, but we more importantly demonstrate that the strength of each approach is highly dependent on the evaluation metric and end-user application. Finally, we show that we can train our neural models to remain very robust to the type of noise expected in real-world data (e.g., typos), while a highly-engineered rule-based system fails entirely.

We study the problem of maximizing a monotone submodular function subject to a cardinality constraint $k$, with the added twist that a number of items $\tau$ from the returned set may be removed. We focus on the worst-case setting considered by Orlin et al.\ (2016), in which a constant-factor approximation guarantee was given for $\tau = o(\sqrt{k})$. In this paper, we solve a key open problem raised therein, presenting a new Partitioned Robust (PRo) submodular maximization algorithm that achieves the same guarantee for more general $\tau = o(k)$. Our algorithm constructs partitions consisting of buckets with exponentially increasing sizes, and applies standard submodular optimization subroutines on the buckets in order to construct the robust solution. We numerically demonstrate the performance of PRo in data summarization and influence maximization, demonstrating gains over both the greedy algorithm and the algorithm of Orlin et al.\ (2016).

In this paper, we investigate general single-index models (SIMs) in high dimensions. Based on U-statistics, we propose two types of robust estimators for the recovery of model parameters, which can be viewed as generalizations of several existing algorithms for one-bit compressed sensing (1-bit CS). With minimal assumption on noise, the statistical guarantees are established for the generalized estimators under suitable conditions, which allow general structures of underlying parameter. Moreover, the proposed estimator is novelly instantiated for SIMs with monotone transfer function, and the obtained estimator can better leverage the monotonicity. Experimental results are provided to support our theoretical analyses.

Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model’s assumptions and reality. We propose a way to systematically detect and mitigate mismatch of a large class of probabilistic models. The idea is to raise the likelihood of each observation to a weight and then to infer both the latent variables and the weights from data. Inferring the weights allows a model to identify observations that match its assumptions and down-weight others. This enables robust inference and improves predictive accuracy. We study four different forms of mismatch with reality, ranging from missing latent groups to structure misspecification. A Poisson factorization analysis of the Movielens 1M dataset shows the benefits of this approach in a practical scenario.

In this paper we analyze the robustness of stochastic variants of the greedy algorithm for submodular maximization. Our main result shows that for maximizing a monotone submodular function under a cardinality constraint, iteratively selecting an element whose marginal contribution is approximately maximal in expectation is a sufficient condition to obtain the optimal approximation guarantee with exponentially high probability, assuming the cardinality is sufficiently large. One consequence of our result is that the linear-time STOCHASTIC-GREEDY algorithm recently proposed in (Mirzasoleiman et al.,2015) achieves the optimal running time while maintaining an optimal approximation guarantee. We also show that high probability guarantees cannot be obtained for stochastic greedy algorithms under matroid constraints, and prove an approximation guarantee which holds in expectation. In contrast to the guarantees of the greedy algorithm, we show that the approximation ratio of stochastic local search is arbitrarily bad, with high probability, as well as in expectation.

We study the problem of estimating the high-dimensional Gaussian graphical model where the data are arbitrarily corrupted. We propose a robust estimator for the sparse precision matrix in the high-dimensional regime. At the core of our method is a robust covariance matrix estimator, which is based on truncated inner product. We establish the statistical guarantee of our estimator on both estimation error and model selection consistency. In particular, we show that provided that the number of corrupted samples $n_2$ for each variable satisfies $n_2 \lesssim \sqrt{n}/\sqrt{\log d}$, where $n$ is the sample size and $d$ is the number of variables, the proposed robust precision matrix estimator attains the same statistical rate as the standard estimator for Gaussian graphical models. In addition, we propose a hypothesis testing procedure to assess the uncertainty of our robust estimator. We demonstrate the effectiveness of our method through extensive experiments on both synthetic data and real-world genomic data.

The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem are rarely known exactly, and using wrong parameters can lead to undesirable outcomes. We hence revisit a continuous version of the Budget Allocation or Bipartite Influence Maximization problem introduced by Alon et al. (2012) from a robust optimization perspective, where an adversary may choose the least favorable parameters within a confidence set. The resulting problem is a nonconvex-concave saddle point problem (or game). We show that this nonconvex problem can be solved exactly by leveraging connections to continuous submodular functions, and by solving a constrained submodular minimization problem. Although constrained submodular minimization is hard in general, here, we establish conditions under which such a problem can be solved to arbitrary precision $\epsilon$.

Deep neural networks coupled with fast simulation and improved computational speeds have led to recent successes in the field of reinforcement learning (RL). However, most current RL-based approaches fail to generalize since: (a) the gap between simulation and real world is so large that policy-learning approaches fail to transfer; (b) even if policy learning is done in real world, the data scarcity leads to failed generalization from training to test scenarios (e.g., due to different friction or object masses). Inspired from H-infinity control methods, we note that both modeling errors and differences in training and test scenarios can just be viewed as extra forces/disturbances in the system. This paper proposes the idea of robust adversarial reinforcement learning (RARL), where we train an agent to operate in the presence of a destabilizing adversary that applies disturbance forces to the system. The jointly trained adversary is reinforced – that is, it learns an optimal destabilization policy. We formulate the policy learning as a zero-sum, minimax objective function. Extensive experiments in multiple environments (InvertedPendulum, HalfCheetah, Swimmer, Hopper, Walker2d and Ant) conclusively demonstrate that our method (a) improves training stability; (b) is robust to differences in training/test conditions; and c) outperform the baseline even in the absence of the adversary.

A popular machine learning strategy is the transfer of a representation (i.e. a feature extraction function) learned on a source task to a target task. Examples include the re-use of neural network weights or word embeddings. We develop sufficient conditions for the success of this approach. If the representation learned from the source task is fixed, we identify conditions on how the tasks relate to obtain an upper bound on target task risk via a VC dimension-based argument. We then consider using the representation from the source task to construct a prior, which is fine-tuned using target task data. We give a PAC-Bayes target task risk bound in this setting under suitable conditions. We show examples of our bounds using feedforward neural networks. Our results motivate a practical approach to weight transfer, which we validate with experiments.

This paper develops a novel tree-based algorithm, called Bonsai, for efficient prediction on IoT devices – such as those based on the Arduino Uno board having an 8 bit ATmega328P microcontroller operating at 16 MHz with no native floating point support, 2 KB RAM and 32 KB read-only flash. Bonsai maintains prediction accuracy while minimizing model size and prediction costs by: (a) developing a tree model which learns a single, shallow, sparse tree with powerful nodes; (b) sparsely projecting all data into a low-dimensional space in which the tree is learnt; and (c) jointly learning all tree and projection parameters. Experimental results on multiple benchmark datasets demonstrate that Bonsai can make predictions in milliseconds even on slow microcontrollers, can fit in KB of memory, has lower battery consumption than all other algorithms while achieving prediction accuracies that can be as much as 30\% higher than state-of-the-art methods for resource-efficient machine learning. Bonsai is also shown to generalize to other resource constrained settings beyond IoT by generating significantly better search results as compared to Bing’s L3 ranker when the model size is restricted to 300 bytes. Bonsai’s code can be downloaded from (http://www.manikvarma.org/code/Bonsai/download.html).

Fisher information and natural gradient provided deep insights and powerful tools to artificial neural networks. However related analysis becomes more and more difficult as the learner’s structure turns large and complex. This paper makes a preliminary step towards a new direction. We extract a local component from a large neural system, and define its relative Fisher information metric that describes accurately this small component, and is invariant to the other parts of the system. This concept is important because the geometry structure is much simplified and it can be easily applied to guide the learning of neural networks. We provide an analysis on a list of commonly used components, and demonstrate how to use this concept to further improve optimization.