While it provides a good foundation to system modeling, analysis, and an understanding of the real world, its application to algorithm design suffers from computational intractability. In this work, we develop a new framework of uncertainty variables to model uncertainty. A simple uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of another variable. We prove Bayes' law and the law of total probability equivalents for uncertainty variables. We define a notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence defined over random variables. We then develop a graphical model, namely Bayesian uncertainty network, a Bayesian network equivalent defined over a collection of uncertainty variables, and show that all the natural conditional independence properties, expected out of a Bayesian network, hold for the Bayesian uncertainty network. We also define the notion of point estimate, and show its relation with the maximum a posteriori estimate.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our objective in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer their modes from observations in real time. The modes can be real or complex. For a real mode, we infer its damping rate, mode shape and amplitude. For a complex mode, we infer its frequency, damping rate, (complex) mode shape and (complex) amplitude. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.

In the Bayesian analysis of signals immersed in noise [1], we seek a representation for the posterior probability of one or more parameters that govern the shape of the signals. Unless the parameter-to-signal map (the forward model) is very simple, the analysis (or inverse solution) comes at significant computational cost, as it requires the stochastic exploration of the likelihood surface at a large number of locations in parameter space. Such is the case, for instance, of parameter estimation for gravitational-wave sources such as the compact binaries detected by LIGO-Virgo [2, 3]; here each likelihood evaluation requires that we generate the gravitational waveform corresponding to a set of source parameters, and compute its noise-weighted correlation with detector data [4]. Waveform generation is usually the costlier operation, so gravitational-wave analysts often utilize faster, less accurate waveform models [5, 6], or accelerated surrogates of slower, more accurate models [7]. Extending the analysis from the data we have to the data we might measure (i.e., characterizing the parameter-estimation prospects of future experiments) compounds the expense, since we need to explore posteriors for many noise realizations, and across the domain of possible source parameters. For concreteness, we price the evaluation of a single Bayesian posterior at null 10 6 times the cost of generating a waveform, and the characterization of parameter-estimation prospects at null 10 6 times the cost of a posterior. With current computational resources, this means that (for instance) accurate component-mass estimates only become available hours or days after the detection of a binary black-hole coalescence [8, 9], while any extensive study of parameter-estimation prospects must rely on less reliable techniques such as the Fisher-matrix approximation [10]. In this Letter, we show how one-or two-dimensional marginalized Bayesian posteriors may be produced using deep neural networks [11] trained on large ensembles of signal noise data streams.

A framework to boost efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation, which we call the refined variational approximation. Its strength lies both in ease of implementation and in automatically tuning the sampler parameters to speed up mixing time. Several strategies to approximate the \emph{evidence lower bound} (ELBO) computation are introduced, including a rewriting of the ELBO objective. A specialization towards state-space models is proposed. Experimental evidence of its efficient performance is shown by solving an influence diagram in a high-dimensional space using a conditional variational autoencoder (cVAE) as a deep Bayes classifier; an unconditional VAE on density estimation tasks; and state-space models for time-series data.

Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random variables. These models have many applications in real-world problems. However, solving these problems requires evaluating the best course of action for each possible outcome of the random variables and hence is computationally challenging. FSCP problems often involve repeated subproblems which ideally should be solved once. In this paper we show how identifying and exploiting these identical subproblems can simplify solving them and leads to a compact representation of the solution. We compile an And-Or search tree to a compact decision diagram. Preliminary experiments show that our proposed method significantly improves the search efficiency by reducing the size of the problem and outperforms the existing methods.

The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also greatly benefit from such mentalizing capabilities. However, humans and systems alike are bound by limitations in their available computational resources. This raises the need for satisficing mentalizing, reconciling accuracy and efficiency in mental state inference that is good enough for a given situation. In this paper, we present different Bayesian models of ToM reasoning and evaluate them based on actual human behavior data that were generated under different kinds of uncertainties. We propose a Switching approach that combines specialized models, embodying simplifying presumptions, in order to achieve a more statisficing mentalizing compared to a Full Bayesian ToM model.

Directed acyclic graphs, or DAGs, are commonly used to repre sent causal relationships in complex biological systems. For example, in gene regulatory ne tworks, directed edges represent regulatory interactions among genes, which are represente d as nodes of the graph. While causal effects in biological networks can be accurately inferred fro m perturbation experiments [33]-- including single or double gene knockouts [30, 42]--these ar e costly to run. Estimating DAGs from observational data is thus an important exploratory ta sk for generating causal hypotheses [10, 15], and designing more efficient experiments. Since the number of possible directed graphs grows super-ex ponentially in the number of nodes, estimation of DAGs is an NPhard problem [6]. Methods of estimating DAGs from observational data can be broadly categorized into three cl asses. The first class, score-based methods, search over the space of all possible graphs, and at tempt to maximize a goodness-of-fit score, generally using a greedy algorithm.

In this work, we introduce a new approach for the efficient solution of autonomous decision and planning problems, with a special focus on decision making under uncertainty and belief space planning (BSP) in high-dimensional state spaces. Usually, to solve the decision problem, we identify the optimal action, according to some objective function. Instead, we claim that we can sometimes generate and solve an analogous yet simplified decision problem, which can be solved more efficiently. Furthermore, a wise simplification method can lead to the same action selection, or one for which the maximal loss can be guaranteed. This simplification is separated from the state inference, and does not compromise its accuracy, as the selected action would finally be applied on the original state. At first, we develop the concept for general decision problems, and provide a theoretical framework of definitions to allow a coherent discussion. We then practically apply these ideas to BSP problems, in which the problem is simplified by considering a sparse approximation of the initial belief. The scalable sparsification algorithm we provide is able to yield solutions which are guaranteed to be consistent with the original problem. We demonstrate the benefits of the approach in the solution of a highly realistic active-SLAM problem, and manage to significantly reduce computation time, with practically no loss in the quality of solution. This rigorous and fundamental work is conceptually novel, and holds numerous possible extensions.

Large textual corpora are often represented by the document-term frequency matrix whose elements are the frequency of terms; however, this matrix has two problems: sparsity and high dimensionality. Four dimension reduction strategies are used to address these problems. Of the four strategies, unsupervised feature transformation (UFT) is a popular and efficient strategy to map the terms to a new basis in the document-term frequency matrix. Although several UFT-based methods have been developed, fuzzy clustering has not been considered for dimensionality reduction. This research explores fuzzy clustering as a new UFT-based approach to create a lower-dimensional representation of documents. Performance of fuzzy clustering with and without using global term weighting methods is shown to exceed principal component analysis and singular value decomposition. This study also explores the effect of applying different fuzzifier values on fuzzy clustering for dimensionality reduction purpose.