We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive. We argue mathematically that full-covariance approximations only improve the ELBO if they improve the expected log-likelihood. We further show that deeper mean-field networks are able to express predictive distributions approximately equivalent to shallower full-covariance networks. We validate these observations empirically, demonstrating that deeper models decrease the divergence between diagonal- and full-covariance Gaussian fits to the true posterior.

With the overwhelming online products available in recent years, there is an increasing need to filter and deliver relevant personalized advice for users. Recommender systems solve this problem by modeling and predicting individual preferences for a great variety of items such as movies, books or research articles. In this chapter, we explore rigorous network-based models that outperform leading approaches for recommendation. The network models we consider are based on the explicit assumption that there are groups of individuals and of items, and that the preferences of an individual for an item are determined only by their group memberships. The accurate prediction of individual user preferences over items can be accomplished by different methodologies, such as Monte Carlo sampling or Expectation-Maximization methods, the latter resulting in a scalable algorithm which is suitable for large datasets.

We present a new operator-free, measure-theoretic definition of the conditional mean embedding as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of marginal distributions has been defined rigorously, the existing operator-based approach of the conditional version lacks a rigorous definition, and depends on strong assumptions that hinder its analysis. Our definition does not impose any of the assumptions that the operator-based counterpart requires. We derive a natural regression interpretation to obtain empirical estimates, and provide a thorough analysis of its properties, including universal consistency. As natural by-products, we obtain the conditional analogues of the Maximum Mean Discrepancy and Hilbert-Schmidt Independence Criterion, and demonstrate their behaviour via simulations.

We address the problem of learning human-interpretable descriptions of a complex system from a finite set of positive and negative examples of its behavior. In contrast to most of the recent work in this area, which focuses on descriptions expressed in Linear Temporal Logic (LTL), we develop a learning algorithm for formulas in the IEEE standard temporal logic PSL (Property Specification Language). Our work is motivated by the fact that many natural properties, such as an event happening at every n-th point in time, cannot be expressed in LTL, whereas it is easy to express such properties in PSL. Moreover, formulas in PSL can be more succinct and easier to interpret (due to the use of regular expressions in PSL formulas) than formulas in LTL. Our learning algorithm builds on top of an existing algorithm for learning LTL formulas. Roughly speaking, our algorithm reduces the learning task to a constraint satisfaction problem in propositional logic and then uses a SAT solver to search for a solution in an incremental fashion. We have implemented our algorithm and performed a comparative study between the proposed method and the existing LTL learning algorithm. Our results illustrate the effectiveness of the proposed approach to provide succinct human-interpretable descriptions from examples.

Feedforward computations, such as evaluating a neural network or sampling from an autoregressive model, are ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parrallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallel iterations. Experimentally, we demonstrate the effectiveness of our approach in accelerating 1) the evaluation of DenseNets on ImageNet and 2) autoregressive sampling of MADE and PixelCNN. We are able to achieve between 1.2 and 33 speedup factors under various conditions and computation models.

Time series clustering is a challenging task due to the specific nature of the data. Classical approaches do not perform well and need to be adapted either through a new distance measure or a data transformation. In this paper we investigate the combination of a convolutional autoencoder and a k-medoids algorithm to perfom time series clustering. The convolutional autoencoder allows to extract meaningful features and reduce the dimension of the data, leading to an improvement of the subsequent clustering. Using simulation and energy related data to validate the approach, experimental results show that the clustering is robust to outliers thus leading to finer clusters than with standard methods.

In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are closely related to certain regions around the density modes, and every cluster corresponds to a bump of the density. The Modal EM algorithm is an iterative procedure that can identify the local maxima of any density function. In this contribution, we propose a fast and efficient Modal EM algorithm to be used when the density function is estimated through a finite mixture of Gaussian distributions with parsimonious component-covariance structures. After describing the procedure, we apply the proposed Modal EM algorithm on both simulated and real data examples, showing its high flexibility in several contexts.

The prevalence of wearable sensors (e.g., smart wristband) is enabling an unprecedented opportunity to not only inform health and wellness states of individuals, but also assess and infer demographic information and personality. This can allow us a deeper personalized insight beyond how many steps we took or what is our heart rate. However, before we can achieve this goal of personalized insight about an individual, we have to resolve a number of shortcomings: 1) wearable-sensory time series is often of variable-length and incomplete due to different data collection periods (e.g., wearing behavior varies by person); 2) inter-individual variability to external factors like stress and environment. This paper addresses these challenges and brings us closer to the potential of personalized insights whether about health or personality or job performance about an individual by developing a novel representation learning algorithm, HeartSpace. Specifically, HeartSpace is capable of encoding time series data with variable-length and missing values via the integration of a time series encoding module and a pattern aggregation network. Additionally, HeartSpace implements a Siamese-triplet network to optimize representations by jointly capturing intra- and inter-series correlations during the embedding learning process. Our empirical evaluation over two different data presents significant performance gains over state-of-the-art baselines in a variety of applications, including personality prediction, demographics inference, user identification.

In this paper, we investigate the non-stationary combinatorial semi-bandit problem, both in the switching case and in the dynamic case. In the general case where (a) the reward function is non-linear, (b) arms may be probabilistically triggered, and (c) only approximate offline oracle exists \cite{wang2017improving}, our algorithm achieves $\tilde{\mathcal{O}}(\sqrt{\mathcal{S} T})$ distribution-dependent regret in the switching case, and $\tilde{\mathcal{O}}(\mathcal{V}^{1/3}T^{2/3})$ in the dynamic case, where $\mathcal S$ is the number of switchings and $\mathcal V$ is the sum of the total ``distribution changes''. The regret bounds in both scenarios are nearly optimal, but our algorithm needs to know the parameter $\mathcal S$ or $\mathcal V$ in advance. We further show that by employing another technique, our algorithm no longer needs to know the parameters $\mathcal S$ or $\mathcal V$ but the regret bounds could become suboptimal. In a special case where the reward function is linear and we have an exact oracle, we design a parameter-free algorithm that achieves nearly optimal regret both in the switching case and in the dynamic case without knowing the parameters in advance.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate that the {\sc BregmanTron} substantially outperforms the {\sc SLIsotron}, and that the loss it learns can be minimized by other algorithms for different tasks, thereby opening the interesting problem of \textit{loss transfer} between domains.