Autonomous vehicles must be comprehensively evaluated before deployed in cities and highways. Current evaluation procedures lack the abilities of weakness-aiming and evolving, thus they could hardly generate adversarial environments for autonomous vehicles, leading to insufficient challenges. To overcome the shortage of static evaluation methods, this paper proposes a novel method to generate adversarial environments with deep reinforcement learning, and to cluster them with a nonparametric Bayesian method. As a representative task of autonomous driving, lane-change is used to demonstrate the superiority of the proposed method. First, two lane-change models are separately developed by a rule-based method and a learning-based method, waiting for evaluation and comparison. Next, adversarial environments are generated by training surrounding interactive vehicles with deep reinforcement learning for local optimal ensembles. Then, a nonparametric Bayesian approach is utilized to cluster the adversarial policies of the interactive vehicles. Finally, the adversarial environment patterns are illustrated and the performances of two lane-change models are evaluated and compared. The simulation results indicate that both models perform significantly worse in adversarial environments than in naturalistic environments, with plenty of weaknesses successfully extracted in a few tests.

In the past twenty years there has been an explosion of the use of graphical models to represent the relationship between a vector of random variables and perform distributed inference which takes advantage of the underlying graphical representations. Bayesian networks (BNs) (Darwiche 2009; Fenton and Neil 2012) are nowadays the most used graphical models, with applications to a wide array of domains and implementation in various software: for instance, the R packages bnlearn by Scutari (2010) and gRain by Højsgaard (2012), among others. However, BNs can only represent symmetric conditional independences which in practical applications may not be fully justified. For this reason, a variety of models that can take into account the asymmetric nature of real-world data have been proposed; for example, context-specific BNs (Boutilier, Friedman, Goldszmidt, and Koller 1996), labeled directed acyclic graphs (Pensar, Nyman, Koski, and Corander 2015) and probabilistic decision graphs (Jaeger, Nielsen, and Silander 2006). Unlike most of its competitors, the chain event graph (CEG) (Collazo, Görgen, and Smith 2018; Smith and Anderson 2008; Riccomagno and Smith 2004, 2009) can capture all (context-specific) conditional independences in a unique graph, obtained by a coalescence over the vertices of an appropriately constructed probability tree, called staged tree.

We study the problem of learning from aggregate observations where supervision signals are given to sets of instances instead of individual instances, while the goal is still to predict labels of unseen individuals. A well-known example is multiple instance learning (MIL). In this paper, we extend MIL beyond binary classification to other problems such as multiclass classification and regression. We present a probabilistic framework that is applicable to a variety of aggregate observations, e.g., pairwise similarity for classification and mean/difference/rank observation for regression. We propose a simple yet effective method based on the maximum likelihood principle, which can be simply implemented for various differentiable models such as deep neural networks and gradient boosting machines. Experiments on three novel problem settings -- classification via triplet comparison and regression via mean/rank observation indicate the effectiveness of the proposed method.

A vital aspect of human intelligence is the ability to compose increasingly complex concepts out of simpler ideas, enabling both rapid learning and adaptation of knowledge. In this paper we show that energy-based models can exhibit this ability by directly combining probability distributions. Samples from the combined distribution correspond to compositions of concepts. For example, given a distribution for smiling faces, and another for male faces, we can combine them to generate smiling male faces. This allows us to generate natural images that simultaneously satisfy conjunctions, disjunctions, and negations of concepts. We evaluate compositional generation abilities of our model on the CelebA dataset of natural faces and synthetic 3D scene images. We also demonstrate other unique advantages of our model, such as the ability to continually learn and incorporate new concepts, or infer compositions of concept properties underlying an image.

We consider the situation where the observed sample contains some observations whose class of origin is known (that is, they are classified with respect to the g underlying classes of interest), and where the remaining observations in the sample are unclassified (that is, their class labels are unknown). For class-conditional distributions taken to be known up to a vector of unknown parameters, the aim is to estimate the Bayes' rule of allocation for the allocation of subsequent unclassified observations. Estimation on the basis of both the classified and unclassified data can be undertaken in a straightforward manner by fitting a g-component mixture model by maximum likelihood (ML) via the EM algorithm in the situation where the observed data can be assumed to be an observed random sample from the adopted mixture distribution. This assumption applies if the missing-data mechanism is ignorable in the terminology pioneered by Rubin (1976). An initial likelihood approach was to use the so-called classification ML approach whereby the missing labels are taken to be parameters to be estimated along with the parameters of the class-conditional distributions. However, as it can lead to inconsistent estimates, the focus of attention switched to the mixture ML approach after the appearance of the EM algorithm (Dempster et al., 1977). Particular attention is given here to the asymptotic relative efficiency (ARE) of the Bayes' rule estimated from a partially classified sample. Lastly, we consider briefly some recent results in situations where the missing label pattern is non-ignorable for the purposes of ML estimation for the mixture model.

Probabilistic circuits (PCs) are a promising avenue for probabilistic modeling, as they permit a wide range of exact and efficient inference routines. Recent ``deep-learning-style'' implementations of PCs strive for a better scalability, but are still difficult to train on real-world data, due to their sparsely connected computational graphs. In this paper, we propose Einsum Networks (EiNets), a novel implementation design for PCs, improving prior art in several regards. At their core, EiNets combine a large number of arithmetic operations in a single monolithic einsum-operation, leading to speedups and memory savings of up to two orders of magnitude, in comparison to previous implementations. As an algorithmic contribution, we show that the implementation of Expectation-Maximization (EM) can be simplified for PCs, by leveraging automatic differentiation. Furthermore, we demonstrate that EiNets scale well to datasets which were previously out of reach, such as SVHN and CelebA, and that they can be used as faithful generative image models.

The stochastic block model (SBM) is a random graph model in which the edges are generated according to the underlying cluster structure on the vertices. The (ferromagnetic) Ising model, on the other hand, assigns $\pm 1$ labels to vertices according to an underlying graph structure in a way that if two vertices are connected in the graph then they are more likely to be assigned the same label. In SBM, one aims to recover the underlying clusters from the graph structure while in Ising model, an extensively-studied problem is to recover the underlying graph structure based on i.i.d. samples (labelings of the vertices). In this paper, we propose a natural composition of SBM and the Ising model, which we call the Stochastic Ising Block Model (SIBM). In SIBM, we take SBM in its simplest form, where $n$ vertices are divided into two equal-sized clusters and the edges are connected independently with probability $p$ within clusters and $q$ across clusters. Then we use the graph $G$ generated by the SBM as the underlying graph of the Ising model and draw $m$ i.i.d. samples from it. The objective is to exactly recover the two clusters in SBM from the samples generated by the Ising model, without observing the graph $G$. As the main result of this paper, we establish a sharp threshold $m^\ast$ on the sample complexity of this exact recovery problem in a properly chosen regime, where $m^\ast$ can be calculated from the parameters of SIBM. We show that when $m\ge m^\ast$, one can recover the clusters from $m$ samples in $O(n)$ time as the number of vertices $n$ goes to infinity. When $m

The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process with infinite horizon. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using heuristic quantum algorithms such as adiabatic quantum annealing and the quantum approximate optimization algorithm on near-term quantum hardware. In proving that the variational minimization of our Hamiltonian is equivalent to the Bellman optimality condition we establish an interesting analogy with classical field theory. Along with proof-of-concept calculations to corroborate our formulation by simulated and quantum annealing against classical Q-Learning, we analyze the scaling of physical resources required to solve our Hamiltonian on quantum hardware.

The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchanges occur through a centralized order book. The goal of the storage device operator is the maximization of the profits received over the entire trading horizon, while taking into account the operational constraints of the unit. The sequential decision-making problem of trading in the intraday market is modelled as a Markov Decision Process. An asynchronous distributed version of the fitted Q iteration algorithm is chosen for solving this problem due to its sample efficiency. The large and variable number of the existing orders in the order book motivates the use of high-level actions and an alternative state representation. Historical data are used for the generation of a large number of artificial trajectories in order to address exploration issues during the learning process. The resulting policy is back-tested and compared against a benchmark strategy that is the current industrial standard. Results indicate that the agent converges to a policy that achieves in average higher total revenues than the benchmark strategy.

The process of discovery in the physical, biological and medical sciences can be painstakingly slow. Most experiments fail, and the time from initiation of research until a new advance reaches commercial production can span 20 years. This tutorial is aimed to provide experimental scientists with a foundation in the science of making decisions. Using numerical examples drawn from the experiences of the authors, the article describes the fundamental elements of any experimental learning problem. It emphasizes the important role of belief models, which include not only the best estimate of relationships provided by prior research, previous experiments and scientific expertise, but also the uncertainty in these relationships. We introduce the concept of a learning policy, and review the major categories of policies. We then introduce a policy, known as the knowledge gradient, that maximizes the value of information from each experiment. We bring out the importance of reducing uncertainty, and illustrate this process for different belief models.