There has been much recent, exciting work on combining the complementary strengths of latent variable models and deep learning. Latent variable modeling makes it easy to explicitly specify model constraints through conditional independence properties, while deep learning makes it possible to parameterize these conditional likelihoods with powerful function approximators. While these "deep latent variable" models provide a rich, flexible framework for modeling many real-world phenomena, difficulties exist: deep parameterizations of conditional likelihoods usually make posterior inference intractable, and latent variable objectives often complicate backpropagation by introducing points of non-differentiability. This tutorial explores these issues in depth through the lens of variational inference.

Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain likelihood ratio with respect to FE's belief state as represented by a probability function on FE's proposition space. Subsequently FE communicates its recently acquired confirmation that a certain evidence proposition is true. Then TOF performs likelihood ratio transfer mediated reasoning thereby revising their own belief state. The logical principles involved in likelihood transfer mediated reasoning are discussed in a setting where probabilistic arithmetic is done within a meadow, and with Adams conditioning placed in a central role.

Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not mutually beneficial, for instance, when tasks are sufficiently dissimilar or change over time. Here, we use the connection between gradient-based meta-learning and hierarchical Bayes (Grant et al., 2018) to propose a mixture of hierarchical Bayesian models over the parameters of an arbitrary function approximator such as a neural network. Generalizing the model-agnostic meta-learning (MAML) algorithm (Finn et al., 2017), we present a stochastic expectation maximization procedure to jointly estimate parameter initializations for gradient descent as well as a latent assignment of tasks to initializations. This approach better captures the diversity of training tasks as opposed to consolidating inductive biases into a single set of hyperparameters. Our experiments demonstrate better generalization performance on the standard miniImageNet benchmark for 1-shot classification. We further derive a novel and scalable non-parametric variant of our method that captures the evolution of a task distribution over time as demonstrated on a set of few-shot regression tasks.

Binary data matrices can represent many types of data such as social networks, votes or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the $[0,1]$ range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage to lead to uninterpretable models. Mean-parameterized NMF, on the contrary, overcomes this problem. We propose a unified framework for Bayesian mean-parameterized nonnegative binary matrix factorization models (NBMF). We analyze three models which correspond to three possible constraints that respect the mean-parametrization without the need for link functions. Furthermore, we derive a novel collapsed Gibbs sampler and a collapsed variational algorithm to infer the posterior distribution of the factors. Next, we extend the proposed models to a nonparametric setting where the number of used latent dimensions is automatically driven by the observed data. We analyze the performance of our NBMF methods in multiple datasets for different tasks such as dictionary learning and prediction of missing data. Experiments show that our methods provide similar or superior results than the state of the art, while automatically detecting the number of relevant components.

As Computer Vision algorithms move from passive analysis of pixels to active reasoning over semantics, the breadth of information algorithms need to reason over has expanded significantly. One of the key challenges in this vein is the ability to identify the information required to make a decision, and select an action that will recover this information. We propose an reinforcement-learning approach that maintains an distribution over its internal information, thus explicitly representing the ambiguity in what it knows, and needs to know, towards achieving its goal. Potential actions are then generated according to particles sampled from this distribution. For each potential action a distribution of the expected answers is calculated, and the value of the information gained is obtained, as compared to the existing internal information. We demonstrate this approach applied to two vision-language problems that have attracted significant recent interest, visual dialogue and visual query generation. In both cases the method actively selects actions that will best reduce its internal uncertainty, and outperforms its competitors in achieving the goal of the challenge.

One of the core challenges in Visual Dialogue problems is asking the question that will provide the most useful information towards achieving the required objective. Encouraging an agent to ask the right questions is difficult because we don't know a-priori what information the agent will need to achieve its task, and we don't have an explicit model of what it knows already. We propose a solution to this problem based on a Bayesian model of the uncertainty in the implicit model maintained by the visual dialogue agent, and in the function used to select an appropriate output. By selecting the question that minimises the predicted regret with respect to this implicit model the agent actively reduces ambiguity. The Bayesian model of uncertainty also enables a principled method for identifying when enough information has been acquired, and an action should be selected. We evaluate our approach on two goal-oriented dialogue datasets, one for visual-based collaboration task and the other for a negotiation-based task. Our uncertainty-aware information-seeking model outperforms its counterparts in these two challenging problems.

Abstract--In this paper we formulate a probabilistic model for class-specific discriminant subspace learning. The proposed model can naturally incorporate the multi-modal structure of the negative class, which is neglected by existing methods. Moreover, it can be directly used to define a probabilistic classification rule in the discriminant subspace. We show that existing class-specific discriminant analysis methods are special cases of the proposed probabilistic model and, by casting them as probabilistic models, they can be extended to class-specific classifiers. We illustrate the performance of the proposed model, in comparison with that of related methods, in both verification and classification problems.

The Dempster-Shafer (DS) Theory (DST) or the Theory of Evidence is considered by many researchers as an appropriate tool to represent various 2 ANDRZEJ MATUSZEWSKI, MIECZYS lAW A. K lOPOTEK aspects of human dealing with uncertain knowledge, especially for representation ofpartial ignorance. However, one particular obstacle in applying DST is its relationship to frequencies [12]. Though, in general a belief function may be derived from frequencies under some particular database representation [5], there exist serious difficulties in finding factorizations of belief functions from data. In probability theory and in classical statistics the factorizations are usually related to notion of (conditional) independence and such possibility istested accordingly. However, in DST conditional belief distributions prove to be non-proper belief functions (that is ones connected with negative "frequencies").This makes statistical testing of potential conditional independencies practically impossible, as no coherent interpretation could be found so far for negative belief function values.

As societies around the world are ageing, the number of Alzheimer's disease (AD) patients is rapidly increasing. To date, no low-cost, non-invasive biomarkers have been established to advance the objectivization of AD diagnosis and progression assessment. Here, we utilize Bayesian neural networks to develop a multivariate predictor for AD severity using a wide range of quantitative EEG (QEEG) markers. The Bayesian treatment of neural networks both automatically controls model complexity and provides a predictive distribution over the target function, giving uncertainty bounds for our regression task. It is therefore well suited to clinical neuroscience, where data sets are typically sparse and practitioners require a precise assessment of the predictive uncertainty. We use data of one of the largest prospective AD EEG trials ever conducted to demonstrate the potential of Bayesian deep learning in this domain, while comparing two distinct Bayesian neural network approaches, i.e., Monte Carlo dropout and Hamiltonian Monte Carlo.

The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed model propagates uncertainty in a principled manner allowing it to learn from small amounts of data and providing predictions with associated uncertainty. We provide experiments that show how our proposed model provides favorable quantitative results compared with the state-of-the-art while simultaneously providing a representation that resides on a low-dimensional interpretable manifold.