We study the online learning problem where a forecaster is trying to predict each day the next bit in a sequence, such as whether the stock market will go up or down. Every morning, for T days, he solicits the opinions of a number n of experts, who each make up or down predictions. Based on their predictions, the forecaster makes a choice between up and down, then buys or sells accordingly. The goal of the forecaster is to make as few mistakes as possible given that the bit sequence may be generated adversarially. This is a classical learning problem that has been studied in a large body of literature starting with the development of Blackwell approachability [Bla56] and Hannan consistency [Han57], and continued in learning theory under the paradigm of combining expert advice [LW94, Vov90]. One of the best known approaches is the Weighted-Majority algorithm [LW94], which keeps track of weights for all the experts and changes them in every round depending on the quality of their predictions. The average number of mistakes made by the forecaster when using such an algorithm can be bounded by the number of mistakes made by the best expert plus log n/T.

Surface reconstruction is a vital tool in a wide range of areas of medical image analysis and clinical research. Despite the fact that many methods have proposed solutions to the reconstruction problem, most, due to their deterministic nature, do not directly address the issue of quantifying uncertainty associated with their predictions. We remedy this by proposing a novel probabilistic deep learning approach capable of simultaneous surface reconstruction and associated uncertainty prediction. The method incorporates prior shape information in the form of a principal component analysis (PCA) model. Experiments using the UK Biobank data show that our probabilistic approach outperforms an analogous deterministic PCA-based method in the task of 2D organ delineation and quantifies uncertainty by formulating distributions over predicted surface vertex positions.

We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov models (KDE-MMs) we discuss are nonlinear, nonparametric, fully probabilistic representations of stationary processes, based on techniques with strong asymptotic consistency properties. The models generate new data by concatenating points from the training data sequences in a context-sensitive manner, together with some additive driving noise. We present novel EM-type maximum-likelihood algorithms for data-driven bandwidth selection in KDE-MMs. Additionally, we augment the KDE-MMs with a hidden state, yielding a new model class, KDE-HMMs. The added state variable captures non-Markovian long memory and signal structure (e.g., slow oscillations), complementing the short-range dependences described by the Markov process. The resulting joint Markov and hidden-Markov structure is appealing for modelling complex real-world processes such as speech signals. We present guaranteed-ascent EM-update equations for model parameters in the case of Gaussian kernels, as well as relaxed update formulas that greatly accelerate training in practice. Experiments demonstrate increased held-out set probability for KDE-HMMs on several challenging natural and synthetic data series, compared to traditional techniques such as autoregressive models, HMMs, and their combinations.

Abstraction plays a key role in concept learning and knowledge discovery. While pervasive in both human and artificial intelligence, it remains mysterious how concepts are abstracted in the first place. We study the nature of abstraction through a group-theoretic approach, formalizing it as a hierarchical, interpretable, and task-free clustering problem. This clustering framework is data-free, feature-free, similarity-free, and globally hierarchical---the four key features that distinguish it from common clustering models. Beyond a theoretical foundation for abstraction, we also present a top-down and a bottom-up approach to establish an algorithmic foundation for practical abstraction-generating methods. Lastly, using both a theoretical explanation and a real-world application, we show that the coupling of our abstraction framework with statistics realizes Shannon's information lattice and even further, brings learning into the picture. This gives a first step towards a principled and cognitive way of automatic concept learning and knowledge discovery.

Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. To provide reliable and interpretable outputs, it requires to be conducted with respect to a suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count-rates. Rather than explicitly modeling the noise distribution, this work proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the $\beta$-divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of $\beta$, in a range covering Gaussian, Poissonian and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of $\beta$ to improve factor analysis.

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

In this paper, we introduce a new model for leveraging unlabeled data to improve generalization performances of image classifiers: a two-branch encoder-decoder architecture called HybridNet. The first branch receives supervision signal and is dedicated to the extraction of invariant class-related representations. The second branch is fully unsupervised and dedicated to model information discarded by the first branch to reconstruct input data. To further support the expected behavior of our model, we propose an original training objective. It favors stability in the discriminative branch and complementarity between the learned representations in the two branches. HybridNet is able to outperform state-of-the-art results on CIFAR-10, SVHN and STL-10 in various semi-supervised settings.

We propose to incorporate adversarial dropout in generative multi-adversarial networks, by omitting or dropping out, the feedback of each discriminator in the framework with some probability at the end of each batch. Our approach forces the single generator not to constrain its output to satisfy a single discriminator, but, instead, to satisfy a dynamic ensemble of discriminators. We show that this leads to a more generalized generator, promoting variety in the generated samples and avoiding the common mode collapse problem commonly experienced with generative adversarial networks (GANs). We further provide evidence that the proposed framework, named Dropout-GAN, promotes sample diversity both within and across epochs, eliminating mode collapse and stabilizing training.

Generating versatile and appropriate synthetic speech requires control over the output expression separate from the spoken text. Important non-textual speech variation is seldom annotated, in which case output control must be learned in an unsupervised fashion. In this paper, we perform an in-depth study of methods for unsupervised learning of control in statistical speech synthesis. For example, we show that popular unsupervised training heuristics can be interpreted as variational inference in certain autoencoder models. We additionally connect these models to VQ-VAEs, another, recently-proposed class of deep variational autoencoders, which we show can be derived from a very similar mathematical argument. The implications of these new probabilistic interpretations are discussed. We illustrate the utility of the various approaches with an application to emotional speech synthesis, where the unsupervised methods for learning expression control (without access to emotional labels) are found to give results that in many aspects match or surpass the previous best supervised approach.

We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic valuations, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We show that the logarithmic query complexity bound also holds for three agents with additive valuations. These results suggest that it is possible to fairly allocate goods in practice even when the number of goods is extremely large. By contrast, we prove that computing an allocation satisfying envy-freeness and another of its relaxations, envy-freeness up to any good (EFX), requires a linear number of queries even when there are only two agents with identical additive valuations.