ICML 2016 论文列表

We initiate the study of low-distortion finite metric embeddings in multi-class (and multi-label) classification where (i) both the space of input instances and the space of output classes have combinatorial metric structure and (ii) the concepts we wish to learn are low-distortion embeddings. We develop new geometric techniques and prove strong learning lower bounds. These provable limits hold even when we allow learners and classifiers to get advice by one or more experts. Our study overwhelmingly indicates that post-geometry assumptions are necessary in multi-class classification, as in natural language processing (NLP). Technically, the mathematical tools we developed in this work could be of independent interest to NLP. To the best of our knowledge, this is the first work which formally studies classification problems in combinatorial spaces. and where the concepts are low-distortion embeddings.

We consider a broad class of first-order optimization algorithms which are \emphoblivious, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as smoothness or strong convexity parameters. With the knowledge of these two parameters, we show that any such algorithm attains an iteration complexity lower bound of Ω(\sqrtL/ε) for L-smooth convex functions, and \tildeΩ(\sqrtL/μ\ln(1/ε)) for L-smooth μ-strongly convex functions. These lower bounds are stronger than those in the traditional oracle model, as they hold independently of the dimension. To attain these, we abandon the oracle model in favor of a structure-based approach which builds upon a framework recently proposed in Arjevani et al. (2015). We further show that without knowing the strong convexity parameter, it is impossible to attain an iteration complexity better than \tildeΩ\sqrt(L/μ)\ln(1/ε). This result is then used to formalize an observation regarding L-smooth convex functions, namely, that the iteration complexity of algorithms employing time-invariant step sizes must be at least Ω(L/ε).

An important question in feature selection is whether a selection strategy recovers the “true” set of features, given enough data. We study this question in the context of the popular Least Absolute Shrinkage and Selection Operator (Lasso) feature selection strategy. In particular, we consider the scenario when the model is misspecified so that the learned model is linear while the underlying real target is nonlinear. Surprisingly, we prove that under certain conditions, Lasso is still able to recover the correct features in this case. We also carry out numerical studies to empirically verify the theoretical results and explore the necessity of the conditions under which the proof holds.

Over the past decade, Monte Carlo Tree Search (MCTS) and specifically Upper Confidence Bound in Trees (UCT) have proven to be quite effective in large probabilistic planning domains. In this paper, we focus on how values are backpropagated in the MCTS tree, and apply complex return strategies from the Reinforcement Learning (RL) literature to MCTS, producing 4 new MCTS variants. We demonstrate that in some probabilistic planning benchmarks from the International Planning Competition (IPC), selecting a MCTS variant with a backup strategy different from Monte Carlo averaging can lead to substantially better results. We also propose a hypothesis for why different backup strategies lead to different performance in particular environments, and manipulate a carefully structured grid-world domain to provide empirical evidence supporting our hypothesis.

The aim of the paper is to provide an exact approach for generating a Poisson process sampled from a hierarchical CRM, without having to instantiate the infinitely many atoms of the random measures. We use completely random measures (CRM) and hierarchical CRM to define a prior for Poisson processes. We derive the marginal distribution of the resultant point process, when the underlying CRM is marginalized out. Using well known properties unique to Poisson processes, we were able to derive an exact approach for instantiating a Poisson process with a hierarchical CRM prior. Furthermore, we derive Gibbs sampling strategies for hierarchical CRM models based on Chinese restaurant franchise sampling scheme. As an example, we present the sum of generalized gamma process (SGGP), and show its application in topic-modelling. We show that one can determine the power-law behaviour of the topics and words in a Bayesian fashion, by defining a prior on the parameters of SGGP.

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade.Despite being popular, very little is known in terms of its theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimization and analyze its performance. We characterize a family of non-convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an ε-approximate solution within O(1 / ε^2) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of “zero-order optimization", and devise a variant of our algorithm which converges at rate of O(d^2/ ε^4).

While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks– \textitInternal Covariate Shift– the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of mean and standard deviation of input (distribution) to hidden layers inaccurate due to shifting parameter values (especially during initial training epochs). Another fundamental problem with BN is that it cannot be used with batch-size 1 during training. We address these drawbacks of BN by proposing a non-adaptive normalization technique for removing covariate shift, that we call \textitNormalization Propagation. Our approach does not depend on batch statistics, but rather uses a data-independent parametric estimate of mean and standard-deviation in every layer thus being computationally faster compared with BN. We exploit the observation that the pre-activation before Rectified Linear Units follow Gaussian distribution in deep networks, and that once the first and second order statistics of any given dataset are normalized, we can forward propagate this normalization without the need for recalculating the approximate statistics for hidden layers.

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel or neural network structure), and are computationally demanding. Interestingly, the theory of nonlinear CCA, without functional restrictions, had been studied in the population setting by Lancaster already in the 1950s, but these results have not inspired practical algorithms. We revisit Lancaster’s theory to devise a practical algorithm for nonparametric CCA (NCCA). Specifically, we show that the solution can be expressed in terms of the singular value decomposition of a certain operator associated with the joint density of the views. Thus, by estimating the population density from data, NCCA reduces to solving an eigenvalue system, superficially like kernel CCA but, importantly, without requiring the inversion of any kernel matrix. We also derive a partially linear CCA (PLCCA) variant in which one of the views undergoes a linear projection while the other is nonparametric. Using a kernel density estimate based on a small number of nearest neighbors, our NCCA and PLCCA algorithms are memory-efficient, often run much faster, and perform better than kernel CCA and comparable to deep CCA.

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.

The Noisy Non-negative Matrix factorization (NMF) is: given a data matrix A (d x n), find non-negative matrices B;C (d x k, k x n respy.) so that A = BC +N, where N is a noise matrix. Existing polynomial time algorithms with proven error guarantees require EACH column N_⋅j to have l1 norm much smaller than ||(BC)_⋅j ||_1, which could be very restrictive. In important applications of NMF such as Topic Modeling as well as theoretical noise models (e.g. Gaussian with high sigma), almost EVERY column of N_.j violates this condition. We introduce the heavy noise model which only requires the average noise over large subsets of columns to be small. We initiate a study of Noisy NMF under the heavy noise model. We show that our noise model subsumes noise models of theoretical and practical interest (for e.g. Gaussian noise of maximum possible sigma). We then devise an algorithm TSVDNMF which under certain assumptions on B,C, solves the problem under heavy noise. Our error guarantees match those of previous algorithms. Our running time of O(k.(d+n)^2) is substantially better than the O(d.n^3) for the previous best. Our assumption on B is weaker than the “Separability” assumption made by all previous results. We provide empirical justification for our assumptions on C. We also provide the first proof of identifiability (uniqueness of B) for noisy NMF which is not based on separability and does not use hard to check geometric conditions. Our algorithm outperforms earlier polynomial time algorithms both in time and error, particularly in the presence of high noise.

Common nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order gradients only). Gating mechanisms that use softly saturating activation functions to emulate the discrete switching of digital logic circuits are good examples of this. We propose to exploit the injection of appropriate noise so that the gradients may flow easily, even if the noiseless application of the activation function would yield zero gradients. Large noise will dominate the noise-free gradient and allow stochastic gradient descent to explore more. By adding noise only to the problematic parts of the activation function, we allow the optimization procedure to explore the boundary between the degenerate saturating) and the well-behaved parts of the activation function. We also establish connections to simulated annealing, when the amount of noise is annealed down, making it easier to optimize hard objective functions. We find experimentally that replacing such saturating activation functions by noisy variants helps optimization in many contexts, yielding state-of-the-art or competitive results on different datasets and task, especially when training seems to be the most difficult, e.g., when curriculum learning is necessary to obtain good results.

We analyze the problem of linear bandits under heavy tailed noise. Most of of the work on linear bandits has been based on the assumption of bounded or sub-Gaussian noise. However, this assumption is often violated in common scenarios such as financial markets. We present two algorithms to tackle this problem: one based on dynamic truncation and one based on a median of means estimator. We show that, when the noise admits admits only a 1 + εmoment, these algorithms are still able to achieve regret in \widetildeO(T^\frac2 + ε2(1 + ε)) and \widetildeO(T^\frac1+ 2ε1 + 3 ε) respectively. In particular, they guarantee sublinear regret as long as the noise has finite variance. We also present empirical results showing that our algorithms achieve a better performance than the current state of the art for bounded noise when the L_∞bound on the noise is large yet the 1 + εmoment of the noise is small.

Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving least squares fitting and hard thresholding. The algorithms are methodologically simple to understand intuitively, computationally easy to implement efficiently, and theoretically appealing for choosing models consistently. Numerical exercises comparing our methods with penalization-based approaches in simulations and data analyses illustrate the great potential of the proposed algorithms.

Crowdsourcing is a very popular means of obtaining the large amounts of labeled data that modern machine learning methods require. Although cheap and fast to obtain, crowdsourced labels suffer from significant amounts of error, thereby degrading the performance of downstream machine learning tasks. With the goal of improving the quality of the labeled data, we seek to mitigate the many errors that occur due to silly mistakes or inadvertent errors by crowdsourcing workers. We propose a two-stage setting for crowdsourcing where the worker first answers the questions, and is then allowed to change her answers after looking at a (noisy) reference answer. We mathematically formulate this process and develop mechanisms to incentivize workers to act appropriately. Our mathematical guarantees show that our mechanism incentivizes the workers to answer honestly in both stages, and refrain from answering randomly in the first stage or simply copying in the second. Numerical experiments reveal a significant boost in performance that such "self-correction" can provide when using crowdsourcing to train machine learning algorithms.

Recent advances in neural variational inference have spawned a renaissance in deep latent variable models. In this paper we introduce a generic variational inference framework for generative and conditional models of text. While traditional variational methods derive an analytic approximation for the intractable distributions over latent variables, here we construct an inference network conditioned on the discrete text input to provide the variational distribution. We validate this framework on two very different text modelling applications, generative document modelling and supervised question answering. Our neural variational document model combines a continuous stochastic document representation with a bag-of-words generative model and achieves the lowest reported perplexities on two standard test corpora. The neural answer selection model employs a stochastic representation layer within an attention mechanism to extract the semantics between a question and answer pair. On two question answering benchmarks this model exceeds all previous published benchmarks.

We present a systematic study on how to morph a well-trained neural network to a new one so that its network function can be completely preserved. We define this as network morphism in this research. After morphing a parent network, the child network is expected to inherit the knowledge from its parent network and also has the potential to continue growing into a more powerful one with much shortened training time. The first requirement for this network morphism is its ability to handle diverse morphing types of networks, including changes of depth, width, kernel size, and even subnet. To meet this requirement, we first introduce the network morphism equations, and then develop novel morphing algorithms for all these morphing types for both classic and convolutional neural networks. The second requirement is its ability to deal with non-linearity in a network. We propose a family of parametric-activation functions to facilitate the morphing of any continuous non-linear activation neurons. Experimental results on benchmark datasets and typical neural networks demonstrate the effectiveness of the proposed network morphism scheme.

The combinatorial explosion that plagues planning and reinforcement learning (RL) algorithms can be moderated using state abstraction. Prohibitively large task representations can be condensed such that essential information is preserved, and consequently, solutions are tractably computable. However, exact abstractions, which treat only fully-identical situations as equivalent, fail to present opportunities for abstraction in environments where no two situations are exactly alike. In this work, we investigate approximate state abstractions, which treat nearly-identical situations as equivalent. We present theoretical guarantees of the quality of behaviors derived from four types of approximate abstractions. Additionally, we empirically demonstrate that approximate abstractions lead to reduction in task complexity and bounded loss of optimality of behavior in a variety of environments.

We consider a variant of the stochastic multi-armed bandit problem, where multiple players simultaneously choose from the same set of arms and may collide, receiving no reward. This setting has been motivated by problems arising in cognitive radio networks, and is especially challenging under the realistic assumption that communication between players is limited. We provide a communication-free algorithm (Musical Chairs) which attains constant regret with high probability, as well as a sublinear-regret, communication-free algorithm (Dynamic Musical Chairs) for the more difficult setting of players dynamically entering and leaving throughout the game. Moreover, both algorithms do not require prior knowledge of the number of players. To the best of our knowledge, these are the first communication-free algorithms with these types of formal guarantees.

As a widely used non-linear activation, Rectified Linear Unit (ReLU) separates noise and signal in a feature map by learning a threshold or bias. However, we argue that the classification of noise and signal not only depends on the magnitude of responses, but also the context of how the feature responses would be used to detect more abstract patterns in higher layers. In order to output multiple response maps with magnitude in different ranges for a particular visual pattern, existing networks employing ReLU and its variants have to learn a large number of redundant filters. In this paper, we propose a multi-bias non-linear activation (MBA) layer to explore the information hidden in the magnitudes of responses. It is placed after the convolution layer to decouple the responses to a convolution kernel into multiple maps by multi-thresholding magnitudes, thus generating more patterns in the feature space at a low computational cost. It provides great flexibility of selecting responses to different visual patterns in different magnitude ranges to form rich representations in higher layers. Such a simple and yet effective scheme achieves the state-of-the-art performance on several benchmarks.