This study provides both analysis and a refined, research-ready implementation of Tang and Kucukelbir's Variational Deep Q Network, a novel approach to maximising the efficiency of exploration in complex learning environments using Variational Bayesian Inference. Alongside reference implementations of both Traditional and Double Deep Q Networks, a small novel contribution is presented - the Double Variational Deep Q Network, which incorporates improvements to increase the stability and robustness of inference-based learning. Finally, an evaluation and discussion of the effectiveness of these approaches is discussed in the wider context of Bayesian Deep Learning.

We present a review and taxonomy of 200 models from the literature on driver behavior modeling. We begin by introducing a mathematical formulation based on the partially observable stochastic game, which serves as a common framework for comparing and contrasting different driver models. Our taxonomy is constructed around the core modeling tasks of state estimation, intention estimation, trait estimation, and motion prediction, and also discusses the auxiliary tasks of risk estimation, anomaly detection, behavior imitation and microscopic traffic simulation. Existing driver models are categorized based on the specific tasks they address and key attributes of their approach.

It is applied to knowledge discovery via dimension reducing and clustering in many fields. However, its generalization error had not been yet clarified since it is a singular statistical model where there is no one to one map from parameters to probability distributions. In this paper, we give the exact asymptotic form of its generalization error and marginal likelihood, by theoretical analysis of its learning coefficient using algebraic geometry. The theoretical result shows that the Bayesian generalization error in LDA is expressed in terms of that in matrix factorization and a penalty from the simplex restriction of LDA's parameter region.

Finding the best model that describes a high dimensional dataset, is a daunting task. For binary data, we show that this becomes feasible, if the search is restricted to simple models. These models -- that we call Minimally Complex Models (MCMs) -- are simple because they are composed of independent components of minimal complexity, in terms of description length. Simple models are easy to infer and to sample from. In addition, model selection within the MCMs' class is invariant with respect to changes in the representation of the data. They portray the structure of dependencies among variables in a simple way. They provide robust predictions on dependencies and symmetries, as illustrated in several examples. MCMs may contain interactions between variables of any order. So, for example, our approach reveals whether a dataset is appropriately described by a pairwise interaction model.

Dynamic discrete choice models are used to estimate the intertemporal preferences of an agent as described by a reward function based upon observable histories of states and implemented actions. However, in many applications, such as reliability and healthcare, the system state is partially observable or hidden (e.g., the level of deterioration of an engine, the condition of a disease), and the decision maker only has access to information imperfectly correlated with the true value of the hidden state. In this paper, we consider the estimation of a dynamic discrete choice model with state variables and system dynamics that are hidden (or partially observed) to both the agent and the modeler, thus generalizing Rust's model to partially observable cases. We analyze the structural properties of the model and prove that this model is still identifiable if the cardinality of the state space, the discount factor, the distribution of random shocks, and the rewards for a given (reference) action are given. We analyze both theoretically and numerically the potential mis-specification errors that may be incurred when Rust's model is improperly used in partially observable settings. We further apply the developed model to a subset of Rust's dataset for bus engine mileage and replacement decisions. The results show that our model can improve model fit as measured by the $\log$-likelihood function by $17.7\%$ and the $\log$-likelihood ratio test shows that our model statistically outperforms Rust's model. Interestingly, our hidden state model also reveals an economically meaningful route assignment behavior in the dataset which was hitherto ignored, i.e. routes with lower mileage are assigned to buses believed to be in worse condition.

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference, and (ii) it allows the incorporation of expert knowledge through rule-based systems. The blending of those two different frameworks can be particularly beneficial for various domains (e.g. engineering), where, even though the significance of uncertainty quantification motivates a Bayesian approach, there is no simple way to incorporate researcher intuition into the model. We validate our models by applying them to synthetic applications: a simple linear regression problem and two more complex structures based on partial differential equations. Finally, we review the advantages of our methodology, which include the simplicity of the implementation, the uncertainty reduction due to the added information and, in some occasions, the derivation of better point predictions, and we address limitations, mainly from the computational complexity perspective, such as the difficulty in choosing an appropriate algorithm and the added computational burden.

Abstract--Bayesian networks are powerful statistical models to study the probabilistic relationships among set random variables with major applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with conditional dependencies, represented as Poisson regression, to model the impact of exogenous variables on the conditional dependencies of the network. We also propose an adaptive regularization method with an intuitive early stopping feature based on density based clustering for efficient learning of the structure and parameters of the proposed network. Using a dataset of patients with multiple chronic conditions extracted from electronic health records of the Department of Veterans Affairs we compare the performance of the proposed approach with some of the existing methods in the literature for both short-term (one-year ahead) and long-term (multi-year ahead) predictions. The proposed approach provides a sparse intuitive representation of the complex functional relationships between multiple chronic conditions. It also provides the capability of analyzing multiple disease trajectories over time given any combination of prior conditions.

In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes approach has recently been proposed, featuring thin-tailed conjugate priors with data-driven centers. While conjugate priors ease some of the computational burden, Markov chain Monte Carlo methods are still needed, which can be expensive when dimension is high. In this paper, we develop a variational approximation to the empirical Bayes posterior that is fast to compute and retains the optimal concentration rate properties of the original. In simulations, our method is shown to have superior performance compared to existing variational approximations in the literature across a wide range of high-dimensional settings.

Solutions to most complex tasks can be decomposed into simpler, intermediate skills, reusable across wider ranges of problems. We follow this concept and introduce Hindsight Off-policy Options (HO2), a new algorithm for efficient and robust option learning. The algorithm relies on critic-weighted maximum likelihood estimation and an efficient dynamic programming inference procedure over off-policy trajectories. We can backpropagate through the inference procedure through time and the policy components for every time-step, making it possible to train all component's parameters off-policy, independently of the data-generating behavior policy. Experimentally, we demonstrate that HO2 outperforms competitive baselines and solves demanding robot stacking and ball-in-cup tasks from raw pixel inputs in simulation. We further compare autoregressive option policies with simple mixture policies, providing insights into the relative impact of two types of abstractions common in the options framework: action abstraction and temporal abstraction. Finally, we illustrate challenges caused by stale data in off-policy options learning and provide effective solutions.

Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria based on pre-defined thresholds over (i) the maximum of the state posterior distribution; and (ii) the state posterior uncertainty are commonly used. In this paper, we propose a geometric interpretation over the state posterior progression and accordingly we provide a point-by-point analysis over the disadvantages of using such conventional termination criteria. For example, through the proposed geometric interpretation we show that confidence thresholds defined over maximum of the state posteriors suffer from stiffness that results in unnecessary evidence collection whereas uncertainty based thresholding methods are fragile to number of categories and terminate prematurely if some state candidates are already discovered to be unfavorable. Moreover, both types of termination methods neglect the evolution of posterior updates. We then propose a new stopping/termination criterion with a geometrical insight to overcome the limitations of these conventional methods and provide a comparison in terms of decision accuracy and speed. We validate our claims using simulations and using real experimental data obtained through a brain computer interfaced typing system.