We present new techniques for automatically constructing probabilistic programs for data analysis, interpretation, and prediction. These techniques work with probabilistic domain-specific data modeling languages that capture key properties of a broad class of data generating processes, using Bayesian inference to synthesize probabilistic programs in these modeling languages given observed data. We provide a precise formulation of Bayesian synthesis for automatic data modeling that identifies sufficient conditions for the resulting synthesis procedure to be sound. We also derive a general class of synthesis algorithms for domain-specific languages specified by probabilistic context-free grammars and establish the soundness of our approach for these languages. We apply the techniques to automatically synthesize probabilistic programs for time series data and multivariate tabular data. We show how to analyze the structure of the synthesized programs to compute, for key qualitative properties of interest, the probability that the underlying data generating process exhibits each of these properties. Second, we translate probabilistic programs in the domain-specific language into probabilistic programs in Venture, a general-purpose probabilistic programming system. The translated Venture programs are then executed to obtain predictions of new time series data and new multivariate data records. Experimental results show that our techniques can accurately infer qualitative structure in multiple real-world data sets and outperform standard data analysis methods in forecasting and predicting new data.

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to form time series prediction models such as non-linear finite-impulse response (NFIR) models as well as non-linear autoregressive (NARX) models. Gaussian process state-space models (GPSS) can be used to learn the dynamic and measurement models for a state-space representation of the input-output data. Temporal and spatio-temporal Gaussian processes can be directly used to form regressor on the data in the time domain. The aim of this article is to briefly outline the main directions in system identification methods using Gaussian processes.

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model Gaussian marginal distributions. To model non-Gaussian data, a GP can be warped by a nonlinear transformation (or warping) as performed by warped GPs (WGPs) and more computationally-demanding alternatives such as Bayesian WGPs and deep GPs. However, the WGP requires a numerical approximation of the inverse warping for prediction, which increases the computational complexity in practice. To sidestep this issue, we construct a novel class of warpings consisting of compositions of multiple elementary functions, for which the inverse is known explicitly. We then propose the compositionally-warped GP (CWGP), a non-Gaussian generative model whose expressiveness follows from its deep compositional architecture, and its computational efficiency is guaranteed by the analytical inverse warping. Experimental validation using synthetic and real-world datasets confirms that the proposed CWGP is robust to the choice of warpings and provides more accurate point predictions, better trained models and shorter computation times than WGP.

Airspace models have played an important role in the development and evaluation of aircraft collision avoidance systems for both manned and unmanned aircraft. As Urban Air Mobility (UAM) systems are being developed, we need new encounter models that are representative of their operational environment. Developing such models is challenging due to the lack of data on UAM behavior in the airspace. While previous encounter models for other aircraft types rely on large datasets to produce realistic trajectories, this paper presents an approach to encounter modeling that instead relies on expert knowledge. In particular, recent advances in preference-based learning are extended to tune an encounter model from expert preferences. The model takes the form of a stochastic policy for a Markov decision process (MDP) in which the reward function is learned from pairwise queries of a domain expert. We evaluate the performance of two querying methods that seek to maximize the information obtained from each query. Ultimately, we demonstrate a method for generating realistic encounter trajectories with only a few minutes of an expert's time.

Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational and statistical efficiency, especially given the need to manage the exploration/exploitation tradeoff. As a result, a core RL question remains open: how can we design provably efficient RL algorithms that incorporate function approximation? This question persists even in a basic setting with linear dynamics and linear rewards, for which only linear function approximation is needed. This paper presents the first provable RL algorithm with both polynomial runtime and polynomial sample complexity in this linear setting, without requiring a "simulator" or additional assumptions. Concretely, we prove that an optimistic modification of Least-Squares Value Iteration (LSVI)---a classical algorithm frequently studied in the linear setting---achieves $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret, where $d$ is the ambient dimension of feature space, $H$ is the length of each episode, and $T$ is the total number of steps. Importantly, such regret is independent of the number of states and actions.

This paper considers the problem of estimating a low-rank matrix from the observation of all, or a subset, of its entries in the presence of Poisson noise. When we observe all the entries, this is a problem of matrix denoising; when we observe only a subset of the entries, this is a problem of matrix completion. In both cases, we exploit an assumption that the underlying matrix is low-rank. Specifically, we analyze several estimators, including a constrained nuclear-norm minimization program, nuclear-norm regularized least squares, and a nonconvex constrained low-rank optimization problem. We show that for all three estimators, with high probability, we have an upper error bound (in the Frobenius norm error metric) that depends on the matrix rank, the fraction of the elements observed, and maximal row and column sums of the true matrix. We furthermore show that the above results are minimax optimal (within a universal constant) in classes of matrices with low rank and bounded row and column sums. We also extend these results to handle the case of matrix multinomial denoising and completion.

We compute exact literal-weighted model counts of CNF formulas. Our algorithm employs dynamic programming, with Algebraic Decision Diagrams as the primary data structure. This technique is implemented in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We also compare ADDMC to state-of-the-art exact model counters (Cachet, c2d, d4, miniC2D, and sharpSAT) on the two largest CNF model counting benchmark families (BayesNet and Planning). ADDMC solves the most benchmarks in total within the given timeout.

We propose a new framework of XGBoost that predicts the entire conditional distribution of a univariate response variable. In particular, XGBoostLSS models all moments of a parametric distribution, i.e., mean, location, scale and shape (LSS), instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distribution, modelling and predicting the entire conditional distribution greatly enhances the flexibility of XGBoost, as it allows to gain additional insight into the data generating process, as well as to create probabilistic forecasts from which prediction intervals and quantiles of interest can be derived. We present both a simulation study and real world examples that demonstrate the benefits of our approach.

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by establishing information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. The use of the lower bound ensures convergence to a local optimum of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multi-modal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.

We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a "purely mathematical formalism, detached from any physical interpretation". We show that the quantum-theoretic framework enables modelling of the "Ellsberg paradox", but it also successfully applies to more concrete human decision-making (DM) tests involving financial, managerial and medical decisions. In particular, we provide a faithful mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from "ambiguity seeking" to "ambiguity aversion", and viceversa, thus exhibiting "hope effects" and "fear effects" in management decisions. The present framework provides a new bold and promising direction towards the development of a unified theory of decisions in the presence of uncertainty.