AISTATS 2020 Papers

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint.The two most commonly used methods to overcome this limitation are 1) the variational sparse approximation which relies on inducing points and 2) the state-space equivalent formulation of Gaussian processes which can be seen as exploiting some sparsity in the precision matrix.In this work, we propose to take the best of both worlds: we show that the inducing point framework is still valid for state space models and that it can bring further computational and memory savings. Furthermore, we provide the natural gradient formulation for the proposed variational parameterisation.Finally, this work makes it possible to use the state-space formulation inside deep Gaussian process models as illustrated in one of the experiments.

We study computational aspects of "relational marginal polytopes" which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of first-order logic formulas, the relational marginal polytope is the set of all points that correspond to expected values of the relational marginal statistics that are realizable. In this paper we study the following two problems: (i) Do domain-liftability results for the partition functions of Markov logic networks (MLNs)carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexity-theoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domain-liftable whenever the computation of the partition function of the respective MLNs is domain-liftable (this result has not been rigorously proven before).

Building on a recent framework for distributionally robust optimization, we consider inverse covariance matrix estimation for multivariate data. A novel notion of Wasserstein ambiguity set is provided that is specifically tailored to this problem, leading to a tractable class of regularized estimators. Penalized likelihood estimators for Gaussian data, specifically the graphical lasso estimator, are special cases. Consequently, a direction connection is made between the radius of the Wasserstein ambiguity and the regularization parameter, so that the level of robustness of the estimator is shown to correspond to the level of confidence with which the ambiguity set contains a distribution with the population covariance. A unique feature of the formulation is that the radius can be expressed in closed-form as a function of the ordinary sample covariance matrix. Taking advantage of this finding, a simple algorithm is developed to determine a regularization parameter for graphical lasso, using only the bootstrapped sample covariance matrices, rendering computationally expensive repeated evaluation of the graphical lasso algorithm unnecessary. Alternatively, the distributionally robust formulation can also quantify the robustness of the corresponding estimator if one uses an off-the-shelf method such as cross-validation. Finally, a numerical study is performed to analyze the robustness of the proposed method relative to other automated tuning procedures used in practice.

Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. Though Monte Carlo estimate is unbiased, it has high variance given a small set of samples; thus can result in a spurious objective function. We adopt the distributionally robust optimization perspective to this problem by maximizing the expected objective under the most adversarial distribution. In particular, we propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose. We demonstrate the empirical effectiveness of our proposed framework in synthetic and real-world problems, and characterize its theoretical convergence via Bayesian regret.

Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is worst-case robust under a specified distributional shift of an uncontrolled covariate. In this paper, we study such a problem when the distributional shift is measured via the maximum mean discrepancy (MMD). For the setting of zeroth-order, noisy optimization, we present a novel distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm provably obtains sub-linear robust regret in various settings that differ in how the uncertain covariate is observed. We demonstrate the robust performance of our method on both synthetic and real-world benchmarks.

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly-used models like the Dirichlet process and the beta-Bernoulli process can be expressed using, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.

Reinforcement learning (RL) in discrete action space is ubiquitous in real-world applications, but its complexity grows exponentially with the action-space dimension, making it challenging to apply existing on-policy gradient based deep RL algorithms efficiently. To effectively operate in multidimensional discrete action spaces, we construct a critic to estimate action-value functions, apply it on correlated actions, and combine these critic estimated action values to control the variance of gradient estimation. We follow rigorous statistical analysis to design how to generate and combine these correlated actions, and how to sparsify the gradients by shutting down the contributions from certain dimensions. These efforts result in a new discrete action on-policy RL algorithm that empirically outperforms related on-policy algorithms relying on variance control techniques. We demonstrate these properties on OpenAI Gym benchmark tasks, and illustrate how discretizing the action space could benefit the exploration phase and hence facilitate convergence to a better local optimal solution thanks to the flexibility of discrete policy.

In this paper, we introduce Differentiable Feature Selection, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e. in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N. This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Our algorithm utilizes higher-order correlations between features and targets for both the N>D and N

Discovering the causal effect of a decision is critical to nearly all forms of decision-making. In particular, it is a key quantity in drug development, in crafting government policy, and when implementing a real-world machine learning system. Given only observational data, confounders often obscure the true causal effect. Luckily, in some cases, it is possible to recover the causal effect by using certain observed variables to adjust for the effects of confounders. However, without access to the true causal model, finding this adjustment requires brute-force search. In this work, we present an algorithm that exploits auxiliary variables, similar to instruments, in order to find an appropriate adjustment by a gradient-based optimization method. We demonstrate that it outperforms practical alternatives in estimating the true causal effect, without knowledge of the full causal graph.

We introduce interactive structure discovery, a generic framework that encompasses many interactive learning settings, including active learning, top-k item identification, interactive drug discovery, and others. We adapt a recently developed active learning algorithm of Tosh and Dasgupta for interactive structure discovery, and show that the new algorithm can be made noise-tolerant and enjoys favorable query complexity bounds.

Variational autoencoders are prominent generative models for modeling discrete data. However, with flexible decoders, they tend to ignore the latent codes. In this paper, we study a VAE model with a deterministic decoder (DD-VAE) for sequential data that selects the highest-scoring tokens instead of sampling. Deterministic decoding solely relies on latent codes as the only way to produce diverse objects, which improves the structure of the learned manifold. To implement DD-VAE, we propose a new class of bounded support proposal distributions and derive Kullback-Leibler divergence for Gaussian and uniform priors. We also study a continuous relaxation of deterministic decoding objective function and analyze the relation of reconstruction accuracy and relaxation parameters. We demonstrate the performance of DD-VAE on multiple datasets, including molecular generation and optimization problems.

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero’th order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes. Our results are the first to target simple regret definitions in adversarial scenarios unveiling a challenge that has been rarely considered in prior work.

Clustering problems are fundamental to unsupervised learning. There is an increased emphasis on \emph{fairness} in machine learning and AI; one representative notion of fairness is that no single demographic group should be over-represented among the cluster-centers. This, and much more general clustering problems, can be formulated with “knapsack" and “partition" constraints. We develop new randomized algorithms targeting such problems, and study two in particular: multi-knapsack median and multi-knapsack center. Our rounding algorithms give new approximation and pseudo-approximation algorithms for these problems. One key technical tool we develop and use, which may be of independent interest, is a new tail bound analogous to Feige (2006) for sums of random variables with unbounded variances. Such bounds are very useful in inferring properties of large networks using few samples.

We demonstrate how easy it is for modern machine-learned systems to violate common deontological ethical principles and social norms such as “favor the less fortunate,” and “do not penalize good attributes.” We propose that in some cases such ethical principles can be incorporated into a machine-learned model by adding shape constraints that constrain the model to respond only positively to relevant inputs. We analyze the relationship between these deontological constraints that act on individuals and the consequentialist group-based fairness goals of one-sided statistical parity and equal opportunity. This strategy works with sensitive attributes that are Boolean or real-valued such as income and age, and can help produce more responsible and trustworthy AI.

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.

In this paper, we are proposing a unified and principled method for both the querying and training processes in deep batch active learning. We are providing theoretical insights from the intuition of modeling the interactive procedure in active learning as distribution matching, by adopting the Wasserstein distance. As a consequence, we derived a new training loss from the theoretical analysis, which is decomposed into optimizing deep neural network parameters and batch query selection through alternative optimization. In addition, the loss for training a deep neural network is naturally formulated as a min-max optimization problem through leveraging the unlabeled data information. Moreover, the proposed principles also indicate an explicit uncertainty-diversity trade-off in the query batch selection. Finally, we evaluate our proposed method on different benchmarks, consistently showing better empirical performances and a better time-efficient query strategy compared to the baselines.

Consensus-based distributed optimization methods have recently been advocated as alternatives to parameter server and ring all-reduce paradigms for large scale training of machine learning models. In this case, each worker maintains a local estimate of the optimal parameter vector and iteratively updates it by averaging the estimates obtained from its neighbors, and applying a correction on the basis of its local dataset. While theoretical results suggest that worker communication topology should have strong impact on the number of epochs needed to converge, previous experiments have shown the opposite conclusion. This paper sheds lights on this apparent contradiction and show how sparse topologies can lead to faster convergence even in the absence of communication delays.

The decentralized stochastic multi-player multi-armed bandit (MP-MAB) problem, where the collision information is not available to the players, is studied in this paper. Building on the seminal work of Boursier and Perchet (2019), we propose error correction synchronization involving communication (EC-SIC), whose regret is shown to approach that of the centralized stochastic MP-MAB with collision information. By recognizing that the communication phase without collision information corresponds to the Z-channel model in information theory, the proposed EC-SIC algorithm applies optimal error correction coding for the communication of reward statistics. A fixed message length, as opposed to the logarithmically growing one in Boursier and Perchet (2019), also plays a crucial role in controlling the communication loss. Experiments with practical Z-channel codes, such as repetition code, flip code and modified Hamming code, demonstrate the superiority of EC-SIC in both synthetic and real-world datasets.

Programming by example is the problem of synthesizing a program from a small set of input / output pairs. Recent works applying machine learning methods to this task show promise, but are typically reliant on generating synthetic examples for training. A particular challenge lies in generating meaningful sets of inputs and outputs, which well-characterize a given program and accurately demonstrate its behavior. Where examples used for testing are generated by the same method as training data then the performance of a model may be partly reliant on this similarity. In this paper we introduce a novel approach using an SMT solver to synthesize inputs which cover a diverse set of behaviors for a given program. We carry out a case study comparing this method to existing synthetic data generation procedures in the literature, and find that data generated using our approach improves both the discriminatory power of example sets and the ability of trained machine learning models to generalize to unfamiliar data.