We propose a models with lower latency and power consumption while Bayesian approach to trend detection in which also ensuring privacy. However, as there is no access to the probability of a keyword being trendy, given actual data from participating devices, it poses a problem a dataset, is computed via Bayes' Theorem; the for the analysis of federated learning models. Federated analytics probability of a dataset, given that a keyword (Ramage & Mazzocchi) is a practice introduced to is trendy, is computed through secure aggregation solve this problem. It uses the same infrastructure as federated of such conditional probabilities over local learning to aggregate the computed metric by each datasets of users. We propose a protocol, named participating device using local data and shared models. SAFE, for Bayesian federated analytics that offers Federated analytics has already gone beyond just measuring sufficient privacy for production-grade use the quality metric to computing descriptive statistics cases and reduces the computational burden of (Ramage & Mazzocchi; Zhu et al., 2020), generating synthetic users and an aggregator. We illustrate this approach data (Xin et al., 2020; Chaulwar, 2020) and learning with a trend detection experiment and discuss new insights (Chen et al., 2019). These methods are generally how this approach could be extended further combined with secure aggregation protocols to ensure to make it production-ready.

We perform approximate inference in state-space models that allow for nonlinear higher-order Markov chains in latent space. The conditional independencies of the generative model enable us to parameterize only an inference model, which learns to estimate clean states in a self-supervised manner using maximum likelihood. First, we propose a recurrent method that is trained directly on noisy observations. Afterward, we cast the model such that the optimization problem leads to an update scheme that backpropagates through a recursion similar to the classical Kalman filter and smoother. In scientific applications, domain knowledge can give a linear approximation of the latent transition maps. We can easily incorporate this knowledge into our model, leading to a hybrid inference approach. In contrast to other methods, experiments show that the hybrid method makes the inferred latent states physically more interpretable and accurate, especially in low-data regimes. Furthermore, we do not rely on an additional parameterization of the generative model or supervision via uncorrupted observations or ground truth latent states. Despite our model's simplicity, we obtain competitive results on the chaotic Lorenz system compared to a fully supervised approach and outperform a method based on variational inference.

Node features and structural information of a graph are both crucial for semi-supervised node classification problems. A variety of graph neural network (GNN) based approaches have been proposed to tackle these problems, which typically determine output labels through feature aggregation. This can be problematic, as it implies conditional independence of output nodes given hidden representations, despite their direct connections in the graph. To learn the direct influence among output nodes in a graph, we propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. To balance model complexity and expressivity, the pairwise factors have a shared component and a separate scaling coefficient for each edge. We apply the EM algorithm to train our model, and utilize a star-shaped piecewise likelihood for the tractable surrogate objective. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear actions for any subset of covariates and under any Bayesian LMM. Crucially, these actions inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian LMM. Rather than selecting a single "best" subset, which is often unstable and limited in its information content, we collect the acceptable family of subsets that nearly match the predictive ability of the "best" subset. The acceptable family is summarized by its smallest member and key variable importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and in both cases demonstrate excellent prediction, estimation, and selection ability.

We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let $\mathcal{P}$ be a causal model on a set $\mathbf{V}$ of observable variables on a given causal graph $G$. For sets $\mathbf{X},\mathbf{Y}\subseteq \mathbf{V}$, and setting ${\bf x}$ to $\mathbf{X}$, let $P_{\bf x}(\mathbf{Y})$ denote the interventional distribution on $\mathbf{Y}$ with respect to an intervention ${\bf x}$ to variables ${\bf x}$. Shpitser and Pearl (AAAI 2006), building on the work of Tian and Pearl (AAAI 2001), gave an exact characterization of the class of causal graphs for which the interventional distribution $P_{\bf x}({\mathbf{Y}})$ can be uniquely determined. We give the first efficient version of the Shpitser-Pearl algorithm. In particular, under natural assumptions, we give a polynomial-time algorithm that on input a causal graph $G$ on observable variables $\mathbf{V}$, a setting ${\bf x}$ of a set $\mathbf{X} \subseteq \mathbf{V}$ of bounded size, outputs succinct descriptions of both an evaluator and a generator for a distribution $\hat{P}$ that is $\varepsilon$-close (in total variation distance) to $P_{\bf x}({\mathbf{Y}})$ where $Y=\mathbf{V}\setminus \mathbf{X}$, if $P_{\bf x}(\mathbf{Y})$ is identifiable. We also show that when $\mathbf{Y}$ is an arbitrary set, there is no efficient algorithm that outputs an evaluator of a distribution that is $\varepsilon$-close to $P_{\bf x}({\mathbf{Y}})$ unless all problems that have statistical zero-knowledge proofs, including the Graph Isomorphism problem, have efficient randomized algorithms.

Predictive coding offers a potentially unifying account of cortical function -- postulating that the core function of the brain is to minimize prediction errors with respect to a generative model of the world. The theory is closely related to the Bayesian brain framework and, over the last two decades, has gained substantial influence in the fields of theoretical and cognitive neuroscience. A large body of research has arisen based on both empirically testing improved and extended theoretical and mathematical models of predictive coding, as well as in evaluating their potential biological plausibility for implementation in the brain and the concrete neurophysiological and psychological predictions made by the theory. Despite this enduring popularity, however, no comprehensive review of predictive coding theory, and especially of recent developments in this field, exists. Here, we provide a comprehensive review both of the core mathematical structure and logic of predictive coding, thus complementing recent tutorials in the literature. We also review a wide range of classic and recent work within the framework, ranging from the neurobiologically realistic microcircuits that could implement predictive coding, to the close relationship between predictive coding and the widely-used backpropagation of error algorithm, as well as surveying the close relationships between predictive coding and modern machine learning techniques.

This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics.

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.

The need to avoid confident predictions on unfamiliar data has sparked interest in out-of-distribution (OOD) detection. It is widely assumed that Bayesian neural networks (BNN) are well suited for this task, as the endowed epistemic uncertainty should lead to disagreement in predictions on outliers. In this paper, we question this assumption and provide empirical evidence that proper Bayesian inference with common neural network architectures does not necessarily lead to good OOD detection. To circumvent the use of approximate inference, we start by studying the infinite-width case, where Bayesian inference can be exact considering the corresponding Gaussian process. Strikingly, the kernels induced under common architectural choices lead to uncertainties that do not reflect the underlying data generating process and are therefore unsuited for OOD detection. Finally, we study finite-width networks using HMC, and observe OOD behavior that is consistent with the infinite-width case. Overall, our study discloses fundamental problems when naively using BNNs for OOD detection and opens interesting avenues for future research.

Reinforcement learning (RL) studies how an agent comes to achieve reward in an environment through interactions over time. Recent advances in machine RL have surpassed human expertise at the world's oldest board games and many classic video games, but they require vast quantities of experience to learn successfully -- none of today's algorithms account for the human ability to learn so many different tasks, so quickly. Here we propose a new approach to this challenge based on a particularly strong form of model-based RL which we call Theory-Based Reinforcement Learning, because it uses human-like intuitive theories -- rich, abstract, causal models of physical objects, intentional agents, and their interactions -- to explore and model an environment, and plan effectively to achieve task goals. We instantiate the approach in a video game playing agent called EMPA (the Exploring, Modeling, and Planning Agent), which performs Bayesian inference to learn probabilistic generative models expressed as programs for a game-engine simulator, and runs internal simulations over these models to support efficient object-based, relational exploration and heuristic planning. EMPA closely matches human learning efficiency on a suite of 90 challenging Atari-style video games, learning new games in just minutes of game play and generalizing robustly to new game situations and new levels. The model also captures fine-grained structure in people's exploration trajectories and learning dynamics. Its design and behavior suggest a way forward for building more general human-like AI systems.