AISTATS 2019 论文列表

We study lifted weight learning of Markov logic networks. We show that there is an algorithm for maximum-likelihood learning of 2-variable Markov logic networks which runs in time polynomial in the domain size. Our results are based on existing lifted-inference algorithms and recent algorithmic results on computing maximum entropy distributions.

In this work, we study a problem arising from two lines of works: online optimization and lifelong learning. In the problem, there is a sequence of tasks arriving sequentially, and within each task, we have to make decisions one after one and then suffer corresponding losses. The tasks are related as they share some common representation, but they are different as each requires a different predictor on top of the representation. As learning a representation is usually costly in lifelong learning scenarios, the goal is to learn it continuously through time across different tasks, making the learning of later tasks easier than previous ones. We provide such learning algorithms with good regret bounds which can be seen as natural generalization of prior works on online optimization.

Function estimation under shape restrictions, such as convexity, has many practical applications and has drawn a lot of recent interests. In this work we argue that convexity, as a global property, is too strict and prone to outliers. Instead, we propose to use weakly convex functions as a simple alternative to quantify “approximate convexity”—a notion that is perhaps more relevant in practice. We prove that, unlike convex functions, weakly convex functions can exactly interpolate any finite dataset and they are universal approximators. Through regularizing the modulus of convexity, we show that weakly convex functions can be efficiently estimated both statistically and algorithmically, requiring minimal modifications to existing algorithms and theory for estimating convex functions. Our numerical experiments confirm the class of weakly convex functions as another competitive alternative for nonparametric estimation.

We introduce algorithms that achieve state-of-the-art dynamic regret bounds for non-stationary linear stochastic bandit setting. It captures natural applications such as dynamic pricing and ads allocation in a changing environment. We show how the difficulty posed by the non-stationarity can be overcome by a novel marriage between stochastic and adversarial bandits learning algorithms. Our main contributions are the tuned Sliding Window UCB (SW-UCB) algorithm with optimal dynamic regret, and the tuning free bandit-over-bandit (BOB) framework built on top of the SW-UCB algorithm with best (compared to existing literature) dynamic regret.

We adapt graphical causal structure learning methods to apply to nonstationary time series data, specifically to processes that exhibit stochastic trends. We modify the likelihood component of the BIC score used by score-based search algorithms, such that it remains a consistent selection criterion for integrated or cointegrated processes. We use this modified score in conjunction with the SVAR-GFCI algorithm, which allows us to recover qualitative structural information about the underlying data-generating process even in the presence of latent (unmeasured) factors. We demonstrate our approach on both simulated and real macroeconomic data.

We provide high-probability sample complexity guarantees for exact structure recovery of tree-structured graphical models, when only noisy observations of the respective vertex emissions are available. We assume that the hidden variables follow either an Ising model or a Gaussian graphical model, and the observables are noise-corrupted versions of the hidden variables: We consider multiplicative $\pm 1$ binary noise for Ising models, and additive Gaussian noise for Gaussian models. Such hidden models arise naturally in a variety of applications such as physics, biology, computer science, and finance. We study the impact of measurement noise on the task of learning the underlying tree structure via the well-known \textit{Chow-Liu algorithm} and provide formal sample complexity guarantees for exact recovery. In particular, for a tree with $p$ vertices and probability of failure $\delta>0$, we show that the number of necessary samples for exact structure recovery is of the order of $\mc{O}(\log(p/\delta))$ for Ising models (which remains the \textit{same as in the noiseless case}), and $\mc{O}(\mathrm{polylog}{(p/\delta)})$ for Gaussian models.

Complex classifiers may exhibit “embarassing” failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is perfectly predictable if the input contains certain features, or rules, and otherwise it is predictable by a linear classifier. We define a hypothesis class that captures this notion and determine its sample complexity. We also give evidence that efficient algorithms cannot achieve this sample complexity. We then derive a simple and efficient algorithm and show that its sample complexity is close to optimal, among efficient algorithms. Experiments on synthetic and sentiment analysis data demonstrate the efficacy of the method, both in terms of accuracy and interpretability.

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of neural networks based on empirical risk minimization, and provide algorithm-dependent guarantees. In particular, we prove that tensor initialization followed by gradient descent can converge to the ground-truth parameters at a linear rate up to some statistical error. To the best of our knowledge, this is the first work characterizing the recovery guarantee for practical learning of one-hidden-layer ReLU networks with multiple neurons. Numerical experiments verify our theoretical findings.

Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a restrictive assumption: the training data is drawn from a Gaussian distribution. In this paper, we provide a novel unified framework to design loss functions with desirable landscape properties for a wide range of general input distributions. On these loss functions, remarkably, stochastic gradient descent theoretically recovers the true parameters with \emph{global} initializations and empirically outperforms the existing approaches. Our loss function design bridges the notion of score functions with the topic of neural network optimization. Central to our approach is the task of estimating the score function from samples, which is of basic and independent interest to theoretical statistics. Traditional estimation methods (example: kernel based) fail right at the outset; we bring statistical methods of local likelihood to design a novel estimator of score functions, that provably adapts to the local geometry of the unknown density.

Programming by examples (PBE) is a rapidly growing subfield of AI, that aims to synthesize user-intended programs using input-output examples from the task. As users can provide only a few I/O examples, capturing user-intent accurately and ranking user-intended programs over other programs is challenging even in the simplest of the domains. Commercially deployed PBE systems often require years of engineering effort and domain expertise to devise ranking heuristics for real-time synthesis of accurate programs. But such heuristics may not cater to new domains, or even to a different segment of users from the same domain. In this work, we develop a novel, real-time, ML-based program ranking algorithm that enables synthesis of natural, user-intended, personalized programs. We make two key technical contributions: 1) a new technique to embed programs in a vector space making them amenable to ML-formulations, 2) a novel formulation that interleaves program search with ranking, enabling real-time synthesis of accurate user-intended programs. We implement our solution in the state-of-the-art PROSE framework. The proposed approach learns the intended program with just {\em one} I/O example in a variety of real-world string/date/number manipulation tasks, and outperforms state-of-the-art neural synthesis methods along multiple metrics.

We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated from the mixture. The problem is well-studied in the parametric setting, i.e., when the component distributions are members of a parametric family - such as Gaussian distributions. In this work, we focus on multivariate mixtures of non-parametric product distributions and propose a two-stage approach which recovers the component distributions of the mixture under a smoothness condition. Our approach builds upon the identifiability properties of the canonical polyadic (low-rank) decomposition of tensors, in tandem with Fourier and Shannon-Nyquist sampling staples from signal processing. We demonstrate the effectiveness of the approach on synthetic and real datasets.

Invariance is an effective prior that has been extensively used to bias supervised learning with a \emph{given} representation of data. In order to learn invariant representations, wavelet and scattering based methods “hard code” invariance over the \emph{entire} sample space, hence restricted to a limited range of transformations. Kernels based on Haar integration also work only on a \emph{group} of transformations. In this work, we break this limitation by designing a new representation learning algorithm that incorporates invariances \emph{beyond transformation}. Our approach, which is based on warping the kernel in a data-dependent fashion, is computationally efficient using random features, and leads to a deep kernel through multiple layers. We apply it to convolutional kernel networks and demonstrate its stability.

Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, therefore the connection structure depends on the information/topic content of the cascade. In this paper we consider the case where we observe a sequence of noisy adjacency matrices triggered by information/events with different topic distributions. We propose a novel latent model using the intuition that a connection is more likely to exist between two nodes if they are interested in similar topics, which are common with the information/event. Specifically, we endow each node with two node-topic vectors: an influence vector that measures how influential/authoritative they are on each topic; and a receptivity vector that measures how receptive/susceptible they are to each topic. We show how these two node-topic structures can be estimated from observed adjacency matrices with theoretical guarantee on estimation error, in cases where the topic distributions of the information/events are known, as well as when they are unknown. Experiments on synthetic and real data demonstrate the effectiveness of our model and superior performance compared to state-of-the-art methods.

Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly learned from data using maximum likelihood estimation (MLE). While fitting observed sets well, MLE for DPPs may also assign high likelihoods to unobserved sets that are far from the true generative distribution of the data. To address this issue, which reduces the quality of the learned model, we introduce a novel optimization problem, Contrastive Estimation (CE), which encodes information about "negative" samples into the basic learning model. CE is grounded in the successful use of negative information in machine-vision and language modeling. Depending on the chosen negative distribution (which may be static or evolve during optimization), CE assumes two different forms, which we analyze theoretically and experimentally. We evaluate our new model on real-world datasets; on a challenging dataset, CE learning delivers a considerable improvement in predictive performance over a DPP learned without using contrastive information.

Learning data representations that are transferable and are fair with respect to certain protected attributes is crucial to reducing unfair decisions while preserving the utility of the data. We propose an information-theoretically motivated objective for learning maximally expressive representations subject to fairness constraints. We demonstrate that a range of existing approaches optimize approximations to the Lagrangian dual of our objective. In contrast to these existing approaches, our objective allows the user to control the fairness of the representations by specifying limits on unfairness. Exploiting duality, we introduce a method that optimizes the model parameters as well as the expressiveness-fairness trade-off. Empirical evidence suggests that our proposed method can balance the trade-off between multiple notions of fairness and achieves higher expressiveness at a lower computational cost.

This paper studies Fenchel-Young losses, a generic way to construct convex loss functions from a regularization function. We analyze their properties in depth, showing that they unify many well-known loss functions and allow to create useful new ones easily. Fenchel-Young losses constructed from a generalized entropy, including the Shannon and Tsallis entropies, induce predictive probability distributions. We formulate conditions for a generalized entropy to yield losses with a separation margin, and probability distributions with sparse support. Finally, we derive efficient algorithms, making Fenchel-Young losses appealing both in theory and practice.

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. To enable accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce hyperbolic SVM, a hyperbolic formulation of support vector machine classifiers, and describe its theoretical connection to the Euclidean counterpart. We also generalize Euclidean kernel SVM to hyperbolic space, allowing nonlinear hyperbolic decision boundaries and providing a geometric interpretation for a certain class of indefinite kernels. Hyperbolic SVM improves classification accuracy in simulation and in real-world problems involving complex networks and word embeddings. Our work enables end-to-end analyses based on the inherent hyperbolic geometry of the data without resorting to ill-fitting tools developed for Euclidean space.

We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to $13.43\times$, and also achieves a $2.36\times$-$12.65\times$ speedup over the state-of-the-art straggler mitigation strategies.

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.