AISTATS 2019 Papers

When the weights in a particle filter are not available analytically, standard resampling methods cannot be employed. To circumvent this problem state-of-the-art algorithms replace the true weights with non-negative unbiased estimates. This algorithm is still valid but at the cost of higher variance of the resulting filtering estimates in comparison to a particle filter using the true weights. We propose here a novel algorithm that allows for resampling according to the true intractable weights when only an unbiased estimator of the weights is available. We demonstrate our algorithm on several examples.

Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method’s performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular networks with a learned structure can generalise better on small datasets, while fully stochastic networks can be more robust to parameter initialisation. The proposed method relies on standard neural variational learning and, unlike randomised architecture search, does not require a retraining of the model, thus keeping the computational overhead at minimum.

In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperparameters that determine measures of simulation discrepancy crucially balance inference accuracy and sample efficiency, yet are difficult to tune. In this paper, we present kernel embedding likelihood-free inference (KELFI), a holistic framework that automatically learns model hyperparameters to improve inference accuracy given limited simulation budget. By leveraging likelihood smoothness with conditional mean embeddings, we nonparametrically approximate likelihoods and posteriors as surrogate densities and sample from closed-form posterior mean embeddings, whose hyperparameters are learned under its approximate marginal likelihood. Our modular framework demonstrates improved accuracy and efficiency on challenging inference problems in ecology.

In many high-throughput experimental design settings, such as those common in biochemical engineering, batched queries are often more cost effective than one-by-one sequential queries. Furthermore, it is often not possible to directly choose items to query. Instead, the experimenter specifies a set of constraints that generates a library of possible items, which are then selected stochastically. Motivated by these considerations, we investigate \emph{Batched Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme for choosing the constraints in order to guide exploration towards items with greater utility. We focus on \emph{site-saturation mutagenesis}, a prototypical setting of BSBO in biochemical engineering, and propose a natural objective function for this problem. Importantly, we show that our objective function can be efficiently decomposed as a difference of submodular functions (DS), which allows us to employ DS optimization tools to greedily identify sets of constraints that increase the likelihood of finding items with high utility. Our experimental results show that our algorithm outperforms common heuristics on both synthetic and two real protein datasets.

This paper deals with bandit online learning, where feedback of unknown delay can emerge in non-stochastic multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function to become available through feedback, and are used to estimate the gradient appearing in the corresponding iterative algorithms. Since the challenging case of feedback with unknown delays prevents one from constructing the sought gradient estimates, existing MAB and BCO algorithms become intractable. Delayed exploration, exploitation, and exponential (DEXP3) iterations, along with delayed bandit gradient descent (DBGD) iterations are developed for MAB and BCO with unknown delays, respectively. Based on a unifying analysis framework, it is established that both DEXP3 and DBGD guarantee an $\tilde{\cal O}\big( \sqrt{K(T+D)} \big)$ regret, where $D$ denotes the delay accumulated over $T$ slots, and $K$ represents the number of arms in MAB or the dimension of decision variables in BCO. Numerical tests using both synthetic and real data validate DEXP3 and DBGD.

Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as variational inference or gradient-based sampling) available for Gaussian models with banded precision. We show that this can efficiently be achieved by equipping an automatic differentiation framework, such as TensorFlow or PyTorch, with some linear algebra operators dedicated to banded matrices. This paper studies the algorithmic aspects of the required operators, details their reverse-mode derivatives, and show that their complexity is linear in the number of observations.

Variational autoencoders (VAEs) learn distributions of high-dimensional data. They model data with a deep latent-variable model and then fit the model by maximizing a lower bound of the log marginal likelihood. VAEs can capture complex distributions, but they can also suffer from an issue known as "latent variable collapse," especially if the likelihood model is powerful. Specifically, the lower bound involves an approximate posterior of the latent variables; this posterior "collapses" when it is set equal to the prior, i.e., when the approximate posterior is independent of the data. While VAEs learn good generative models, latent variable collapse prevents them from learning useful representations. In this paper, we propose a simple new way to avoid latent variable collapse by including skip connections in our generative model; these connections enforce strong links between the latent variables and the likelihood function. We study generative skip models both theoretically and empirically. Theoretically, we prove that skip models increase the mutual information between the observations and the inferred latent variables. Empirically, we study images (MNIST and Omniglot) and text (Yahoo). Compared to existing VAE architectures, we show that generative skip models maintain similar predictive performance but lead to less collapse and provide more meaningful representations of the data.

This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X , the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a generalization bound, and shedding light on its connection with Kernel Principal Component Analysis. The proposed algorithms are then detailed at length: they crucially rely on the form taken by the minimizers, revealed by a dedicated Representer Theorem. Finally, numerical experiments on both simulated data and real labeled graphs (molecules) provide empirical evidence of the KAE performances.

AutoML has become a popular service that is provided by most leading cloud service providers today. In this paper, we focus on the AutoML problem from the \emph{service provider’s perspective}, motivated by the following practical consideration: When an AutoML service needs to serve {\em multiple users} with {\em multiple devices} at the same time, how can we allocate these devices to users in an efficient way? We focus on GP-EI, one of the most popular algorithms for automatic model selection and hyperparameter tuning, used by systems such as Google Vizer. The technical contribution of this paper is the first multi-device, multi-tenant algorithm for GP-EI that is aware of \emph{multiple} computation devices and multiple users sharing the same set of computation devices. Theoretically, given $N$ users and $M$ devices, we obtain a regret bound of $O((\text{\bf {MIU}}(T,K) + M)\frac{N^2}{M})$, where $\text{\bf {MIU}}(T,K)$ refers to the maximal incremental uncertainty up to time $T$ for the covariance matrix $K$. Empirically, we evaluate our algorithm on two applications of automatic model selection, and show that our algorithm significantly outperforms the strategy of serving users independently. Moreover, when multiple computation devices are available, we achieve near-linear speedup when the number of users is much larger than the number of devices.

Advances in unsupervised learning enable reconstruction and generation of samples from complex distributions, but this success is marred by the inscrutability of the representations learned. We propose an information-theoretic approach to characterizing disentanglement and dependence in representation learning using multivariate mutual information, also called total correlation. The principle of Total Cor-relation Ex-planation (CorEx) has motivated successful unsupervised learning applications across a variety of domains but under some restrictive assumptions. Here we relax those restrictions by introducing a flexible variational lower bound to CorEx. Surprisingly, we find this lower bound is equivalent to the one in variational autoencoders (VAE) under certain conditions. This information-theoretic view of VAE deepens our understanding of hierarchical VAE and motivates a new algorithm, AnchorVAE, that makes latent codes more interpretable through information maximization and enables generation of richer and more realistic samples.

Bayesian inference for Factorial Hidden Markov Models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We introduce a general purpose ensemble Markov Chain Monte Carlo (MCMC) technique to improve on existing poorly mixing samplers. This is achieved by combining parallel tempering and an auxiliary variable scheme to exchange information between the chains in an efficient way. The latter exploits a genetic algorithm within an augmented Gibbs sampler. We compare our technique with various existing samplers in a simulation study as well as in a cancer genomics application, demonstrating the improvements obtained by our augmented ensemble approach.

Word vector representations are well developed tools for various NLP and Machine Learning tasks and are known to retain significant semantic and syntactic structure of languages. But they are prone to carrying and amplifying bias which can perpetrate discrimination in various applications. In this work, we explore new simple ways to detect the most stereotypically gendered words in an embedding and remove the bias from them. We verify how names are masked carriers of gender bias and then use that as a tool to attenuate bias in embeddings. Further, we extend this property of names to show how names can be used to detect other types of bias in the embeddings such as bias based on race, ethnicity, and age.

In machine learning, models that generalize better often generate outputs that lie on a low-dimensional manifold. Recently, several works have separately shown finite-time manifold identification by some proximal methods. In this work we provide a unified view by giving a simple condition under which any proximal method using a constant step size can achieve finite-iteration manifold detection. For several key methods (FISTA, DRS, ADMM, SVRG, SAGA, and RDA) we give an iteration bound, characterized in terms of their variable convergence rate and a problem-dependent constant that indicates problem degeneracy. For popular models, this constant is related to certain data assumptions, which gives intuition as to when lower active set complexity may be expected in practice.

We analyze the regret of combinatorial Thompson sampling (CTS) for the combinatorial multi-armed bandit with probabilistically triggered arms under the semi-bandit feedback setting. We assume that the learner has access to an exact optimization oracle but does not know the expected base arm outcomes beforehand. When the expected reward function is Lipschitz continuous in the expected base arm outcomes, we derive $O(\sum_{i =1}^m \log T / (p_i \Delta_i))$ regret bound for CTS, where $m$ denotes the number of base arms, $p_i$ denotes the minimum non-zero triggering probability of base arm $i$ and $\Delta_i$ denotes the minimum suboptimality gap of base arm $i$. We also compare CTS with combinatorial upper confidence bound (CUCB) via numerical experiments on a cascading bandit problem.

We apply network Lasso to semi-supervised regression problems involving network-structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regression model, which is motivated by a clustering hypothesis, we provide an analysis of the estimation error incurred by network Lasso. This analysis reveals conditions on the network structure and the available training data which guarantee network Lasso to be accurate. Remarkably, the accuracy of network Lasso is related to the existence of sufficiently large network flows over the empirical graph. Thus, our analysis reveals a connection between network Lasso and maximum network flow problems.

Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest training sequences. Our key insight is to formulate sequential machine teaching as a time-optimal control problem. This allows us to solve sequential teaching by leveraging key theoretical and computational tools developed over the past 60 years in the optimal control community. Specifically, we study the Pontryagin Maximum Principle, which yields a necessary condition for opti- mality of a training sequence. We present analytic, structural, and numerical implica- tions of this approach on a case study with a least-squares loss function and gradient de- scent learner. We compute optimal train- ing sequences for this problem, and although the sequences seem circuitous, we find that they can vastly outperform the best available heuristics for generating training sequences.

We derive an algorithm that achieves the optimal (up to constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent with Tsallis entropy regularizer. We provide a complete characterization of such algorithms and show that Tsallis entropy with power $\alpha = 1/2$ achieves the goal. In addition, the proposed algorithm enjoys improved regret guarantees in two intermediate regimes: the moderately contaminated stochastic regime defined by Seldin and Slivkins [22] and the stochastically constrained adversary studied by Wei and Luo [26]. The algorithm also obtains adversarial and stochastic optimality in the utility-based dueling bandit setting. We provide empirical evaluation of the algorithm demonstrating that it outperforms Ucb1 and Exp3 in stochastic environments. In certain adversarial regimes the algorithm significantly outperforms Ucb1 and Thompson Sampling, which exhibit close to linear regret.

We develop an optimal primal-dual first-order algorithm for a class of stochastic three-composite convex minimization problems. The convergence rate of our method not only improves upon the existing methods, but also matches a lower bound derived for all first-order methods that solve this problem. We extend our proposed algorithm to solve a composite stochastic program with any finite number of nonsmooth functions. In addition, we generalize an optimal stochastic alternating direction method of multipliers (SADMM) algorithm proposed for the two-composite case to solve this problem, and establish its connection to our optimal primal-dual algorithm. We perform extensive numerical experiments on a variety of machine learning applications to demonstrate the superiority of our method via-a-vis the state-of-the-art.