As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and actuation errors compound to the errors introduced while estimating features of the environment. We present a novel approach (1) to incorporate these uncertainties for robot state estimation and (2) to compute the probability of collision pertaining to the estimated robot configurations. The expression for collision probability is obtained as an infinite series and we prove its convergence. An upper bound for the truncation error is also derived and the number of terms required is demonstrated by analyzing the convergence for different robot and obstacle configurations. We evaluate our approach using two simulation domains which use a roadmap-based strategy to synthesize trajectories that satisfy collision probability bounds.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of interest are nonlinear, yet the majority of available techniques for feature selection and sensor placement rely on assumptions of linearity or simple statistical models. We show that when these assumptions are violated, standard techniques can lead to costly over-sensing without guaranteeing that the desired information can be recovered from the measurements. In order to remedy these problems, we introduce a novel data-driven approach for sensor placement and feature selection for a general type of nonlinear inverse problem based on the information contained in secant vectors between data points. Using the secant-based approach, we develop three efficient greedy algorithms that each provide different types of robust, near-minimal reconstruction guarantees. We demonstrate them on two problems where linear techniques consistently fail: sensor placement to reconstruct a fluid flow formed by a complicated shock-mixing layer interaction and selecting fundamental manifold learning coordinates on a torus.

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct neural systems. Characterizing the way in which neural systems reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian model-based characterization of latent brain states and showcase a novel method based on posterior predictive discrepancy using the latent block model to detect transitions between latent brain states in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions.

In recent years it has become clear that the brain maintains a temporal memory of recent events stretching far into the past. This paper presents a neurally-inspired algorithm to use a scale-invariant temporal representation of the past to predict a scale-invariant future. The result is a scale-invariant estimate of future events as a function of the time at which they are expected to occur. The algorithm is time-local, with credit assigned to the present event by observing how it affects the prediction of the future. To illustrate the potential utility of this approach, we test the model on simultaneous renewal processes with different time scales. The algorithm scales well on these problems despite the fact that the number of states needed to describe them as a Markov process grows exponentially.

We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the \emph{maximum-likelihood estimator} (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an \emph{all-or-nothing} (AoN) phase transition, already established for the minimum mean-square-error estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and second-moment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result.

This article focuses on numerical issues in maximum likelihood parameter estimation for Gaussian process regression (GPR). This article investigates the origin of the numerical issues and provides simple but effective improvement strategies. This work targets a basic problem but a host of studies, particularly in the literature of Bayesian optimization, rely on off-the-shelf GPR implementations. For the conclusions of these studies to be reliable and reproducible, robust GPR implementations are critical.

Feature attribution is widely used in interpretable machine learning to explain how influential each measured input feature value is for an output inference. However, measurements can be uncertain, and it is unclear how the awareness of input uncertainty can affect the trust in explanations. We propose and study two approaches to help users to manage their perception of uncertainty in a model explanation: 1) transparently show uncertainty in feature attributions to allow users to reflect on, and 2) suppress attribution to features with uncertain measurements and shift attribution to other features by regularizing with an uncertainty penalty. Through simulation experiments, qualitative interviews, and quantitative user evaluations, we identified the benefits of moderately suppressing attribution uncertainty, and concerns regarding showing attribution uncertainty. This work adds to the understanding of handling and communicating uncertainty for model interpretability.

Discovery and recognition of Group Activities (GA) based on imagery data processing have significant applications in persistent surveillance systems, which play an important role in some Internet services. The process is involved with analysis of sequential imagery data with spatiotemporal associations. Discretion of video imagery requires a proper inference system capable of discriminating and differentiating cohesive observations and interlinking them to known ontologies. We propose an Ontology based GAR with a proper inference model that is capable of identifying and classifying a sequence of events in group activities. A multi-layered Hidden Markov Model (HMM) is proposed to recognize different levels of abstract GA. The multi-layered HMM consists of N layers of HMMs where each layer comprises of M number of HMMs running in parallel. The number of layers depends on the order of information to be extracted. At each layer, by matching and correlating attributes of detected group events, the model attempts to associate sensory observations to known ontology perceptions. This paper demonstrates and compares performance of three different implementation of HMM, namely, concatenated N-HMM, cascaded C-HMM and hybrid H-HMM for building effective multi-layered HMM.

The lack of explainability of a decision from an Artificial Intelligence (AI) based "black box" system/model, despite its superiority in many real-world applications, is a key stumbling block for adopting AI in many high stakes applications of different domain or industry. While many popular Explainable Artificial Intelligence (XAI) methods or approaches are available to facilitate a human-friendly explanation of the decision, each has its own merits and demerits, with a plethora of open challenges. We demonstrate popular XAI methods with a mutual case study/task (i.e., credit default prediction), analyze for competitive advantages from multiple perspectives (e.g., local, global), provide meaningful insight on quantifying explainability, and recommend paths towards responsible or human-centered AI using XAI as a medium. Practitioners can use this work as a catalog to understand, compare, and correlate competitive advantages of popular XAI methods. In addition, this survey elicits future research directions towards responsible or human-centric AI systems, which is crucial to adopt AI in high stakes applications.