In this paper, three recently introduced reinforcement learning (RL) methods are used to generate human-interpretable policies for the cart-pole balancing benchmark. The novel RL methods learn human-interpretable policies in the form of compact fuzzy controllers and simple algebraic equations. The representations as well as the achieved control performances are compared with two classical controller design methods and three non-interpretable RL methods. All eight methods utilize the same previously generated data batch and produce their controller offline - without interaction with the real benchmark dynamics. The experiments show that the novel RL methods are able to automatically generate well-performing policies which are at the same time human-interpretable. Furthermore, one of the methods is applied to automatically learn an equation-based policy for a hardware cart-pole demonstrator by using only human-player-generated batch data. The solution generated in the first attempt already represents a successful balancing policy, which demonstrates the methods applicability to real-world problems.

Few-shot classification (FSC), the task of adapting a classifier to unseen classes given a small labeled dataset, is an important step on the path toward human-like machine learning. Bayesian methods are well-suited to tackling the fundamental issue of overfitting in the few-shot scenario because they allow practitioners to specify prior beliefs and update those beliefs in light of observed data. Contemporary approaches to Bayesian few-shot classification maintain a posterior distribution over model parameters, which is slow and requires storage that scales with model size. Instead, we propose a Gaussian process classifier based on a novel combination of P\'olya-gamma augmentation and the one-vs-each softmax approximation that allows us to efficiently marginalize over functions rather than model parameters. We demonstrate improved accuracy and uncertainty quantification on both standard few-shot classification benchmarks and few-shot domain transfer tasks.

In this paper, we show that slow feature analysis (SFA), a common time series decomposition method, naturally fits into the flow-based models (FBM) framework, a type of invertible neural latent variable models. Building upon recent advances on blind source separation, we show that such a fit makes the time series decomposition identifiable.

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. In this text, we examine the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. We demonstrate that, although standard ensembling techniques certainly help to boost accuracy, the calibration of deep-ensembles relies on subtle trade-offs. Our main finding is that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that, in the low data regime, this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems when compared to standard deep-ensembles.

Exchange algorithm is one of the most popular extensions of Metropolis-Hastings algorithm to sample from doubly-intractable distributions. However, theoretical exploration of exchange algorithm is very limited. For example, natural questions like `Does exchange algorithm converge at a geometric rate?' or `Does the exchange algorithm admit a Central Limit Theorem?' have not been answered. In this paper, we study the theoretical properties of exchange algorithm, in terms of asymptotic variance and convergence speed. We compare the exchange algorithm with the original Metropolis-Hastings algorithm and provide both necessary and sufficient conditions for geometric ergodicity of the exchange algorithm, which can be applied to various practical applications such as exponential random graph models and Ising models. A central limit theorem for the exchange algorithm is also established. Meanwhile, a concrete example, involving the Binomial model with conjugate and non-conjugate priors, is treated in detail with sharp convergence rates. Our results justify the theoretical usefulness of the exchange algorithm.

Both frequentist and Bayesian probability have a role to play in machine learning. For example, if dealing with truly random and discrete variables, such as landing a six in a die roll, the traditional approach of simply calculating the odds (frequency) is the fastest way to model a likely outcome. However, if the six keeps coming up far more often than the predicated 1/6 odds, only Bayesian probability would take that new observation into account and increase the confidence level that someone is playing with loaded dice.

Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory named physics regularized Gaussian process (PRGP), this study presents a stochastic microscopic traffic model that can capture the randomness and measure errors in the real world. Physical knowledge from classical car-following models is converted as physics regularizers, in the form of shadow Gaussian process (GP), of a multivariate PRGP for improving the modeling accuracy. More specifically, a Bayesian inference algorithm is developed to estimate the mean and kernel of GPs, and an enhanced latent force model is formulated to encode physical knowledge into stochastic processes. Also, based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is developed to maximize the evidence lower-bound of the system likelihood. To evaluate the performance of the proposed models, this study conducts empirical studies on real-world vehicle trajectories from the NGSIM dataset. Since one unique feature of the proposed framework is the capability of capturing both car-following and lane-changing behaviors with one single model, numerical tests are carried out with two separated datasets, one contains lane-changing maneuvers and the other doesn't. The results show the proposed method outperforms the previous influential methods in estimation precision.

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function. We propose a new parameter fitting method, Minimum Probability Flow (MPF), which is applicable to any parametric model. We demonstrate parameter estimation using MPF in two cases: a continuous state space model, and an Ising spin glass. In the latter case it outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters.

Of these, probably the most common is the use of supervised classification to construct low-dimensional event summaries, which are informative to carry out statistical inference for a given set of parameters of interest. The learned summary statistics -functions of the data that are informative on their relevant properties-can efficiently combine high-dimensional information from each event into one or a few variables which can be used as the basis of statistical inference. The informational source for this compression are simulated observations produced by a complex generative model; the latter reproduces the chain of physical processes occurring in subatomic collisions and the subsequent interaction of the produced final state particles with the detection elements.

Recent advances in computational methods, material science, and manufacturing technologies reveal promising potentials for using geometrically complex parts to optimize the performance of structural systems. However, this potential has not yet been activated partly due to the immaturity of nondestructive testing (NDT) of such complex parts. Process compensated resonance testing (PCRT) is one of the methods that are in the focus of researchers for this purpose. The key to success for the PCRT approach is to use high-frequency vibration data in conjunction with statistical pattern recognition methods for supervised classification of parts in terms of their structural quality. In this paper, a multi classifier selection-fusion framework based on the Dempster-Shafer theory is proposed. Two new weighting approaches are introduced to enhance the fusion performance, and as such the classification performance. The effectiveness of the proposed framework is validated by its application to six UCI machine learning datasets and one experimental dataset collected from polycrystalline Nickel alloy first-stage turbine blades with a variety of damage features. Comparison with four state-of-the-art fusion techniques shows the good performance of the introduced classifier selection-fusion framework.