We analyze the complexity of learning directed acyclic graphical models from observational data in general settings without specific distributional assumptions. Our approach is information-theoretic and uses a local Markov boundary search procedure in order to recursively construct ancestral sets in the underlying graphical model. Perhaps surprisingly, we show that for certain graph ensembles, a simple forward greedy search algorithm (i.e. without a backward pruning phase) suffices to learn the Markov boundary of each node. This substantially improves the sample complexity, which we show is at most polynomial in the number of nodes. This is then applied to learn the entire graph under a novel identifiability condition that generalizes existing conditions from the literature. As a matter of independent interest, we establish finite-sample guarantees for the problem of recovering Markov boundaries from data. Moreover, we apply our results to the special case of polytrees, for which the assumptions simplify, and provide explicit conditions under which polytrees are identifiable and learnable in polynomial time. We further illustrate the performance of the algorithm, which is easy to implement, in a simulation study. Our approach is general, works for discrete or continuous distributions without distributional assumptions, and as such sheds light on the minimal assumptions required to efficiently learn the structure of directed graphical models from data.

R\'enyi's information provides a theoretical foundation for tractable and data-efficient non-parametric density estimation, based on pair-wise evaluations in a reproducing kernel Hilbert space (RKHS). This paper extends this framework to parametric probabilistic modeling, motivated by the fact that R\'enyi's information can be estimated in closed-form for Gaussian mixtures. Based on this special connection, a novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible, because costs are scale-invariant, avoiding high gradient variance while imposing less restrictions on absolute continuity, which is a huge advantage in parametric information theoretic optimization. The implementation employs a single neural network driven by an orthonormal input appended to a single white noise source adapted to learn an infinite Gaussian mixture model (IMoG), which provides an empirically tractable model distribution in low dimensions. To train SGM, we provide three novel variational cost functions, based on R\'enyi's second-order entropy and divergence, to implement minimization of cross-entropy, minimization of variational representations of $f$-divergence, and maximization of the evidence lower bound (conditional probability). We test the framework for estimation of mutual information and compare the results with the mutual information neural estimation (MINE), for density estimation, for conditional probability estimation in Markov models as well as for training adversarial networks. Our preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as the performance of generative adversarial networks.

Ingenious e-Brain Solutions forecasts that artificial intelligence will transform the cars in the near future as many companies such as Hyundai, Lear Corporation, Yamaha, Volkswagen, and others are working around different AI algorithms and have developed their solutions at various stages (ideation or concept, prototype, pre-commercialized, and commercial). In the automotive industry, AI provides solutions to drivers or passengers to relieve stress, discomfort, anxiety, drowsiness, maintaining temperature, humidity, weather, climate, and improving visualizations. The AI technologies used are machine learning, deep learning, neural network, facial recognition, bayesian network, fuzzy logic, and classification algorithm. In this report, the use of artificial intelligence or any other computational algorithm for the wellbeing or comfort of passengers and drivers is highlighted along with some of their technology development partners, solutions from other industries such as healthcare, aerospace, entertainment, and others which can be implemented in the automotive industry are listed, along with some other sections which are listed in the table of content of the report. The key players profiled in the report are Tesla, Toyota, Volkswagen, Nio, Daimler, General Motors, BMW, Stellantis, Honda, and Hyundai.

The uncertainty of the energy generated by photovoltaic systems incurs an additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This investigation aims to decrease the additional cost by introducing probabilistic multi-task intra-hour solar forecasting (feasible in real time applications) to increase the penetration of photovoltaic systems in power grids. The direction of moving clouds is estimated in consecutive sequences of sky images by extracting features of cloud dynamics with the objective of forecasting the global solar irradiance that reaches photovoltaic systems. The sky images are acquired using a low-cost infrared sky imager mounted on a solar tracker. The solar forecasting algorithm is based on kernel learning methods, and uses the clear sky index as predictor and features extracted from clouds as feature vectors. The proposed solar forecasting algorithm achieved 16.45\% forecasting skill 8 minutes ahead with a resolution of 15 seconds. In contrast, previous work reached 15.4\% forecasting skill with the resolution of 1 minute. Therefore, this solar forecasting algorithm increases the performances with respect to the state-of-the-art, providing grid operators with the capability of managing the inherent uncertainties of power grids with a high penetration of photovoltaic systems.

As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score which is widely used in biostatistics and sufficient for TEs; i.e., we build a generative prognostic model. We prove that the latent variable recovers a prognostic score, and the model identifies individualized treatment effects. The model is then learned as \beta-Intact-VAE--a new type of variational autoencoder (VAE). We derive the TE error bounds that enable representations balanced for treatment groups conditioned on individualized features. The proposed method is compared with recent methods using (semi-)synthetic datasets.

This paper investigates the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) could be generated by a canonical family of SCMs with the same causal diagram where unobserved (exogenous) variables are discrete with a finite domain. Utilizing the canonical SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query. Solving such polynomial programs is in general computationally expensive. We therefore develop effective Monte Carlo algorithms to approximate the optimal bounds from an arbitrary combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.

Graphical models, used to express conditional dependence between random variables observed at various nodes, are used extensively in many fields such as genetics, neuroscience, and social network analysis. While most current statistical methods for estimating graphical models focus on scalar data, there is interest in estimating analogous dependence structures when the data observed at each node are functional, such as signals or images. In this paper, we propose a fully Bayesian regularization scheme for estimating functional graphical models. We first consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019). We then propose a regularization strategy via the graphical horseshoe. We compare these approaches via simulation study and apply our proposed functional graphical horseshoe to two motivating applications, electroencephalography data for comparing brain activation between an alcoholic group and controls, as well as changes in structural connectivity in the presence of traumatic brain injury (TBI). Our results yield insight into how the brain attempts to compensate for disconnected networks after injury.

Surface roughness is primary measure of pavement performance that has been associated with ride quality and vehicle operating costs. Of all the surface roughness indicators, the International Roughness Index (IRI) is the most widely used. However, it is costly to measure IRI, and for this reason, certain road classes are excluded from IRI measurements at a network level. Higher levels of distresses are generally associated with higher roughness. However, for a given roughness level, pavement data typically exhibits a great deal of variability in the distress types, density, and severity. It is hypothesized that it is feasible to estimate the IRI of a pavement section given its distress types and their respective densities and severities. To investigate this hypothesis, this paper uses data from in-service pavements and machine learning methods to ascertain the extent to which IRI can be predicted given a set of pavement attributes. The results suggest that machine learning can be used reliably to estimate IRI based on the measured distress types and their respective densities and severities. The analysis also showed that IRI estimated this way depends on the pavement type and functional class. The paper also includes an exploratory section that addresses the reverse situation, that is, estimating the probability of pavement distress type distribution and occurrence severity/extent based on a given roughness level.

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. Stochastic differential equations (SDEs) are a natural extension to ordinary differential equations which allows modelling of noisy and uncertain driving forces. These models are particularly appealing due to their flexibility in expressing highly complex relationships with simple equations, while retaining a high degree of interpretability. Much work has been done over the last century focussing on understanding and modelling with SDEs, particularly in dynamical systems and quantitative finance (Pavliotis, 2014; Malliavin & Thalmaier, 2006).

Sum-Product Networks (SPNs) are expressive probabilistic models that provide exact, tractable inference. They achieve this efficiency by making used of local independence. On the other hand, mixtures of exchangeable variable models (MEVMs) are a class of tractable probabilistic models that make use of exchangeability of random variables to render inference tractable. Exchangeability, which arises naturally in systems consisting of multiple, interrelated entities, has not been considered for efficient representation and inference in SPNs yet. The contribution of this paper is a novel probabilistic model which we call Exchangeability-Aware Sum-Product Networks (XSPNs). It contains both SPNs and MEVMs as special cases, and combines the ability of SPNs to efficiently learn deep probabilistic models with the ability of MEVMs to efficiently handle exchangeable random variables. We also introduce a structure learning algorithm for XSPNs and empirically show that they can be more accurate and efficient than conventional SPNs when the data contains repeated, interchangeable parts.