Goal recognition design (GRD) facilitates understanding the goals of acting agents through the analysis and redesign of goal recognition models, thus offering a solution for assessing and minimizing the maximal progress of any agent in the model before goal recognition is guaranteed. In a nutshell, given a model of a domain and a set of possible goals, a solution to a GRD problem determines (1) the extent to which actions performed by an agent within the model reveal the agent’s objective; and (2) how best to modify the model so that the objective of an agent can be detected as early as possible. This approach is relevant to any domain in which rapid goal recognition is essential and the model design can be controlled. Applications include intrusion detection, assisted cognition, computer games, and human-robot collaboration. A GRD problem has two components: the analyzed goal recognition setting, and a design model specifying the possible ways the environment in which agents act can be modified so as to facilitate recognition. This work formulates a general framework for GRD in deterministic and partially observable environments, and offers a toolbox of solutions for evaluating and optimizing model quality for various settings. For the purpose of evaluation we suggest the worst case distinctiveness (WCD) measure, which represents the maximal cost of a path an agent may follow before its goal can be inferred by a goal recognition system. We offer novel compilations to classical planning for calculating WCD in settings where agents are bounded-suboptimal. We then suggest methods for minimizing WCD by searching for an optimal redesign strategy within the space of possible modifications, and using pruning to increase efficiency. We support our approach with an empirical evaluation that measures WCD in a variety of GRD settings and tests the efficiency of our compilation-based methods for computing it. We also examine the effectiveness of reducing WCD via redesign and the performance gain brought about by our proposed pruning strategy.

Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk. With the aid of the state-augmentation transformation (SAT), we show that, the two risks can be estimated in Markov decision processes (MDPs) with a stochastic transition-based reward and a randomized policy. To relieve the enlarged state space, a novel definition of isotopic states is proposed for state lumping, considering the special structure of the transformed transition probability. In the numerical experiment, we illustrate state lumping in the SAT, errors from a naive reward simplification, and the validity of the SAT for the two risk estimations.

We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is based on a novel notion of \emph{algebraic independence} of the expert functions. Drawing on optimal transport theory, we establish a connection between the algebraic independence and a certain class of partial differential equations (PDEs). Exploiting this connection allows us to derive convergence rates and minimax lower bounds for parameter estimation.

We propose a neural network architecture, called TransNet, that combines planning and model learning for solving Partially Observable Markov Decision Processes (POMDPs) with non-uniform system dynamics. The past decade has seen a substantial advancement in solving POMDP problems. However, constructing a suitable POMDP model remains difficult. Recently, neural network architectures have been proposed to alleviate the difficulty in acquiring such models. Although the results are promising, existing architectures restrict the type of system dynamics that can be learned --that is, system dynamics must be the same in all parts of the state space. TransNet relaxes such a restriction. Key to this relaxation is a novel neural network module that classifies the state space into classes and then learns the system dynamics of the different classes. TransNet uses this module together with the overall architecture of QMDP-Net[1] to allow solving POMDPs that have more expressive dynamic models, while maintaining efficient data requirement. Its evaluation on typical benchmarks in robot navigation with initially unknown system and environment models indicates that TransNet substantially out-performs the quality of the generated policies and learning efficiency of the state-of-the-art method QMDP-Net.

We present a scheme for sequential decision making with a risk-sensitive objective and constraints in a dynamic environment. A neural network is trained as an approximator of the mapping from parameter space to space of risk and policy with risk-sensitive constraints. For a given risk-sensitive problem, in which the objective and constraints are, or can be estimated by, functions of the mean and variance of return, we generate a synthetic dataset as training data. Parameters defining a targeted process might be dynamic, i.e., they might vary over time, so we sample them within specified intervals to deal with these dynamics. We show that: i). Most risk measures can be estimated using return variance; ii). By virtue of the state-augmentation transformation, practical problems modeled by Markov decision processes with stochastic rewards can be solved in a risk-sensitive scenario; and iii). The proposed scheme is validated by a numerical experiment.

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and further applying this identified surrogate to uncertainty analysis remains to be very challenging. A deep learning approach is presented to provide predictions based on limited and noisy data. To address noise perturbation, the Bayesian learning method that naturally facilitates an automatic updating mechanism is considered to quantify and propagate model uncertainties into predictive quantities. Specifically, hierarchical Bayesian modeling (HBM) is first adopted to describe model uncertainties, which allows the prior assumption to be less subjective, while also makes the proposed surrogate more robust. Next, the Bayesian inference is seamlessly integrated into the DL framework, which in turn supports probabilistic programming by yielding a probability distribution of the quantities of interest rather than their point estimates. Variational inference (VI) is implemented for the posterior distribution analysis where the intractable marginalization of the likelihood function over parameter space is framed in an optimization format, and stochastic gradient descent method is applied to solve this optimization problem. Finally, Monte Carlo simulation is used to obtain an unbiased estimator in the predictive phase of Bayesian inference, where the proposed Bayesian deep learning (BDL) scheme is able to offer confidence bounds for the output estimation by analyzing propagated uncertainties. The effectiveness of Bayesian shrinkage is demonstrated in improving predictive performance using contaminated data, and various examples are provided to illustrate concepts, methodologies, and algorithms of this proposed BDL modeling technique.

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions. These factorizations include non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models, and Born machines, which are naturally related to local quantum circuits. When used to model probability distributions, they exhibit tractable likelihoods and admit efficient learning algorithms. Interestingly, we prove that there exist probability distributions for which there are unbounded separations between the resource requirements of some of these tensor-network factorizations. Particularly surprising is the fact that using complex instead of real tensors can lead to an arbitrarily large reduction in the number of parameters of the network. Additionally, we introduce locally purified states (LPS), a new factorization inspired by techniques for the simulation of quantum systems, with provably better expressive power than all other representations considered. The ramifications of this result are explored through numerical experiments. Our findings imply that LPS should be considered over hidden Markov models, and furthermore provide guidelines for the design of local quantum circuits for probabilistic modeling.

Semi-supervised learning (SSL) uses unlabeled data for training and has been shown to greatly improve performances when compared to a supervised approach on the labeled data available. This claim depends both on the amount of labeled data available and on the algorithm used. In this paper, we compute analytically the gap between the best fully-supervised approach on labeled data and the best semi-supervised approach using both labeled and unlabeled data. We quantify the best possible increase in performance obtained thanks to the unlabeled data, i.e. we compute the accuracy increase due to the information contained in the unlabeled data. Our work deals with a simple high-dimensional Gaussian mixture model for the data in a Bayesian setting. Our rigorous analysis builds on recent theoretical breakthroughs in high-dimensional inference and a large body of mathematical tools from statistical physics initially developed for spin glasses.

Causal estimation relies on separating the variation in the outcome due to the confounders from that due to the treatment. To achieve this separation, practitioners can use external sources of randomness that only influence the treatment called instrumental variables (IVs). Traditional IV-methods rely on structural assumptions that limit the effect that the confounders can have on both outcome and treatment. To relax these assumptions we develop a new estimator called the generalized control-function method (GCFN). GCFN's first stage called variational decoupling (VDE) recovers the residual variation in the treatment given the IV. In the second stage, GCFN regresses the outcome on the treatment and residual variation to compute the causal effect. We evaluate GCFN on simulated data and on recovering the causal effect of slave export on community trust. We show how VDE can help unify IV-estimators and non-IV-estimators.

Traditionally, the automatic recognition of human activities is performed with supervised learning algorithms on limited sets of specific activities. This work proposes to recognize recurrent activity patterns, called routines, instead of precisely defined activities. The modeling of routines is defined as a metric learning problem, and an architecture, called SS2S, based on sequence-to-sequence models is proposed to learn a distance between time series. This approach only relies on inertial data and is thus non intrusive and preserves privacy. Experimental results show that a clustering algorithm provided with the learned distance is able to recover daily routines.