Sleep constitutes a key indicator of human health, performance, and quality of life. Sleep deprivation has long been related to the onset, development, and worsening of several mental and metabolic disorders, constituting an essential marker for preventing, evaluating, and treating different health conditions. Sleep Activity Recognition methods can provide indicators to assess, monitor, and characterize subjects' sleep-wake cycles and detect behavioral changes. In this work, we propose a general method that continuously operates on passively sensed data from smartphones to characterize sleep and identify significant sleep episodes. Thanks to their ubiquity, these devices constitute an excellent alternative data source to profile subjects' biorhythms in a continuous, objective, and non-invasive manner, in contrast to traditional sleep assessment methods that usually rely on intrusive and subjective procedures. A Heterogeneous Hidden Markov Model is used to model a discrete latent variable process associated with the Sleep Activity Recognition task in a self-supervised way. We validate our results against sleep metrics reported by tested wearables, proving the effectiveness of the proposed approach and advocating its use to assess sleep without more reliable sources.

In this work, we address the problem of long-distance navigation for battery electric vehicles (BEVs), where one or more charging sessions are required to reach the intended destination. We consider the availability and performance of the charging stations to be unknown and stochastic, and develop a combinatorial semi-bandit framework for exploring the road network to learn the parameters of the queue time and charging power distributions. Within this framework, we first outline a pre-processing for the road network graph to handle the constrained combinatorial optimization problem in an efficient way. Then, for the pre-processed graph, we use a Bayesian approach to model the stochastic edge weights, utilizing conjugate priors for the one-parameter exponential and two-parameter gamma distributions, the latter of which is novel to multi-armed bandit literature. Finally, we apply combinatorial versions of Thompson Sampling, BayesUCB and Epsilon-greedy to the problem. We demonstrate the performance of our framework on long-distance navigation problem instances in country-sized road networks, with simulation experiments in Norway, Sweden and Finland.

Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show that such representation allows to formulate the statistical Bayesian learning problem in different coordinate systems on the sample space. We further show that such representation allows to learn projections of density operators using a kernel trick. In particular, the study highlights that decomposing wave functions rather than probability densities, as it is done in kernel embedding, allows to preserve the nature of probability operators. Results are illustrated with a simple example using discrete orthogonal wavelet transform of density operators.

Table of contents: What is Conformal Prediction? What is Conformal Prediction used for? Why should I use Conformal Prediction? Why shouldn’t I use Conformal Prediction? How can Conformal Prediction be used in Finance? How can Conformal Prediction be used in Algorithmic Trading? What are some Conformal Prediction alternatives? Understanding Conformal Prediction What is MAPIE? How […]

This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional data (e.g. point cloud data) centred around some lower dimensional unknown manifolds. The geometry of manifold is in general different from the usual Euclidean geometry. Naively applying traditional smoothing methods such as Euclidean Gaussian Processes (GPs) to manifold valued data and so ignoring the geometry of the space can potentially lead to highly misleading predictions and inferences. A manifold embedded in a high dimensional Euclidean space can be well described by a probabilistic mapping function and the corresponding latent space. We investigate the geometrical structure of the unknown manifolds using the Bayesian Gaussian Processes latent variable models(BGPLVM) and Riemannian geometry. The distribution of the metric tensor is learned using BGPLVM. The boundary of the resulting manifold is defined based on the uncertainty quantification of the mapping. We use the the probabilistic metric tensor to simulate Brownian Motion paths on the unknown manifold. The heat kernel is estimated as the transition density of Brownian Motion and used as the covariance functions of GPUM. The applications of GPUM are illustrated in the simulation studies on the Swiss roll, high dimensional real datasets of WiFi signals and image data examples. Its performance is compared with the Graph Laplacian GP, Graph Matern GP and Euclidean GP.

Recent developments using End-to-End Deep Learning models have been shown to have near or better performance than state of the art Recurrent Neural Networks (RNNs) on Automatic Speech Recognition tasks. These models tend to be lighter weight and require less training time than traditional RNN-based approaches. However, these models take frequentist approach to weight training. In theory, network weights are drawn from a latent, intractable probability distribution. We introduce BayesSpeech for end-to-end Automatic Speech Recognition. BayesSpeech is a Bayesian Transformer Network where these intractable posteriors are learned through variational inference and the local reparameterization trick without recurrence. We show how the introduction of variance in the weights leads to faster training time and near state-of-the-art performance on LibriSpeech-960.

Estimating the effect of a treatment on an outcome is a fundamental problem in many fields such as medicine [33, 34, 61], public policy [20] and more [2, 37]. For example, doctors might be interested in how a treatment, such as a drug, affects the recovery of patients [18], economists may be interested in how a job training program affects employment prospectives [35], and advertisers may want to model the average effect an advertisement has on sales [36]. However, individuals may react differently to the treatment of interest, and knowing only the average treatment effect in the population is insufficient. For example, a drug may have adverse effects on some individuals but not others [61], or a person's education and background may affect how much they benefit from job training [35, 50]. Measuring the extent to which different individuals react differently to treatment is known as heterogeneous treatment effect (HTE) estimation. Traditionally, HTE estimation has been done through subgroup analysis [9, 19]. However, this can lead to cherry-picking since the practitioner is the one who identifies subgroups for estimating effects. Recently, there has been more focus on data-driven estimation of heterogeneous treatment effects by letting the data identify which features are important for treatment effect estimation using machine learning techniques [28, 39, 61, 69]. A straightforward approach is to create interaction terms between all covariates and use them in a regression [6].

Simulating the human mobility and generating large-scale trajectories are of great use in many real-world applications, such as urban planning, epidemic spreading analysis, and geographic privacy protect. Although many previous works have studied the problem of trajectory generation, the continuity of the generated trajectories has been neglected, which makes these methods useless for practical urban simulation scenarios. To solve this problem, we propose a novel two-stage generative adversarial framework to generate the continuous trajectory on the road network, namely TS-TrajGen, which efficiently integrates prior domain knowledge of human mobility with model-free learning paradigm. Specifically, we build the generator under the human mobility hypothesis of the A* algorithm to learn the human mobility behavior. For the discriminator, we combine the sequential reward with the mobility yaw reward to enhance the effectiveness of the generator. Finally, we propose a novel two-stage generation process to overcome the weak point of the existing stochastic generation process. Extensive experiments on two real-world datasets and two case studies demonstrate that our framework yields significant improvements over the state-of-the-art methods.

Mesoscale structures are an integral part of the abstraction and analysis of complex systems. They reveal a node's function in the network, and facilitate our understanding of the network dynamics. For example, they can represent communities in social or citation networks, roles in corporate interactions, or core-periphery structures in transportation networks. We usually detect mesoscale structures under the assumption of independence of interactions. Still, in many cases, the interactions invalidate this assumption by occurring in a specific order. Such patterns emerge in pathway data; to capture them, we have to model the dependencies between interactions using higher-order network models. However, the detection of mesoscale structures in higher-order networks is still under-researched. In this work, we derive a Bayesian approach that simultaneously models the optimal partitioning of nodes in groups and the optimal higher-order network dynamics between the groups. In synthetic data we demonstrate that our method can recover both standard proximity-based communities and role-based groupings of nodes. In synthetic and real world data we show that it can compete with baseline techniques, while additionally providing interpretable abstractions of network dynamics.

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical models for tensor-variate data and summarization of complex time-varying texts using topic models. This work advances the state-of-the-art in several directions. First, it introduces a new class of tensor-variate Gaussian graphical models via the Sylvester tensor equation. Second, it develops an optimization technique based on a fast-converging proximal alternating linearized minimization method, which scales tensor-variate Gaussian graphical model estimations to modern big-data settings. Third, it connects Kronecker-structured (inverse) covariance models with spatio-temporal partial differential equations (PDEs) and introduces a new framework for ensemble Kalman filtering that is capable of tracking chaotic physical systems. Fourth, it proposes a modular and interpretable framework for unsupervised and weakly-supervised probabilistic topic modeling of time-varying data that combines generative statistical models with computational geometric methods. Throughout, practical applications of the methodology are considered using real datasets. This includes brain-connectivity analysis using EEG data, space weather forecasting using solar imaging data, longitudinal analysis of public opinions using Twitter data, and mining of mental health related issues using TalkLife data. We show in each case that the graphical modeling framework introduced here leads to improved interpretability, accuracy, and scalability.