Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal with noisy log-likelihood evaluations, such as those arising from simulation-based models. We introduce new `global' acquisition functions, such as expected information gain (EIG) and variational interquantile range (VIQR), which are robust to noise and can be efficiently evaluated within the VBMC setting. In a novel, challenging, noisy-inference benchmark comprising of a variety of models with real datasets from computational and cognitive neuroscience, VBMC+VIQR achieves state-of-the-art performance in recovering the ground-truth posteriors and model evidence. In particular, our method vastly outperforms `local' acquisition functions and other surrogate-based inference methods while keeping a small algorithmic cost. Our benchmark corroborates VBMC as a general-purpose technique for sample-efficient black-box Bayesian inference also with noisy models.

In this paper we present a Bayesian reinforcement learning framework that allows robotic manipulators to adaptively recover from random mechanical failures autonomously, hence being survivable. To this end, we formulate the framework of Bayesian Policy Morphing (BPM) that enables a robot agent to self-modify its learned policy after the diminution of its maneuvering dimensionality. We build upon existing actor-critic framework, and extend it to perform policy gradient updates as posterior learning, taking past policy updates as prior distributions. We show that policy search, in the direction biased by prior experience, significantly improves learning efficiency in terms of sampling requirements. We demonstrate our results on an 8-DOF robotic arm with our algorithm of BPM, while intentionally disabling random joints with different damage types like unresponsive joints, constant offset errors and angular imprecision. Our results have shown that, even with physical damages, the robotic arm can still successfully maintain its functionality to accurately locate and grasp a given target object.

Choosing a publication venue for an academic paper is a crucial step in the research process. However, in many cases, decisions are based on the experience of researchers, which often leads to suboptimal results. Although some existing methods recommend publication venues, they just recommend venues where a paper is likely to be published. In this study, we aim to recommend publication venues from a different perspective. We estimate the number of citations a paper will receive if the paper is published in each venue and recommend the venue where the paper has the most potential impact. However, there are two challenges to this task. First, a paper is published in only one venue, and thus, we cannot observe the number of citations the paper would receive if the paper were published in another venue. Secondly, the contents of a paper and the publication venue are not statistically independent; that is, there exist selection biases in choosing publication venues. In this paper, we propose to use a causal inference method to estimate the treatment effects of choosing a publication venue effectively and to recommend venues based on the potential influence of papers.

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players' strategies and realized payoffs using Bayes's rule. Players adjust their strategies by accounting for an equilibrium strategy or a best response strategy based on the updated belief. We prove that beliefs and strategies converge to a fixed point with probability 1. We also provide conditions that guarantee local and global stability of fixed points. Any fixed point belief consistently estimates the payoff distribution given the fixed point strategy profile. However, convergence to a complete information Nash equilibrium is not always guaranteed. We provide a sufficient and necessary condition under which fixed point belief recovers the unknown parameter. We also provide a sufficient condition for convergence to complete information equilibrium even when parameter learning is incomplete.

In this study, we propose a novel extended target tracking algorithm which is capable of representing the extent of dynamic objects as an ellipsoid with a time-varying orientation angle. A diagonal positive semi-definite matrix is defined to model objects' extent within the random matrix framework where the diagonal elements have inverse-Gamma priors. The resulting measurement equation is non-linear in the state variables, and it is not possible to find a closed-form analytical expression for the true posterior because of the absence of conjugacy. We use the variational Bayes technique to perform approximate inference, where the Kullback-Leibler divergence between the true and the approximate posterior is minimized by performing fixed-point iterations. The update equations are easy to implement, and the algorithm can be used in real-time tracking applications. We illustrate the performance of the method in simulations and experiments with real data. The proposed method outperforms the state-of-the-art methods when compared with respect to accuracy and robustness.

The thesis explores the role machine learning methods play in creating intuitive computational models of neural processing. Combined with interpretability techniques, machine learning could replace human modeler and shift the focus of human effort to extracting the knowledge from the ready-made models and articulating that knowledge into intuitive descroptions of reality. This perspective makes the case in favor of the larger role that exploratory and data-driven approach to computational neuroscience could play while coexisting alongside the traditional hypothesis-driven approach. We exemplify the proposed approach in the context of the knowledge representation taxonomy with three research projects that employ interpretability techniques on top of machine learning methods at three different levels of neural organization. The first study (Chapter 3) explores feature importance analysis of a random forest decoder trained on intracerebral recordings from 100 human subjects to identify spectrotemporal signatures that characterize local neural activity during the task of visual categorization. The second study (Chapter 4) employs representation similarity analysis to compare the neural responses of the areas along the ventral stream with the activations of the layers of a deep convolutional neural network. The third study (Chapter 5) proposes a method that allows test subjects to visually explore the state representation of their neural signal in real time. This is achieved by using a topology-preserving dimensionality reduction technique that allows to transform the neural data from the multidimensional representation used by the computer into a two-dimensional representation a human can grasp. The approach, the taxonomy, and the examples, present a strong case for the applicability of machine learning methods to automatic knowledge discovery in neuroscience.

We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node's state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise random variable. This paper focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.

Low-rank tensor decomposition is one of the most effective approaches to reduce the memory and computing requirements of large-size neural networks, enabling their efficient deployment on various hardware platforms. While post-training tensor compression can greatly reduce the cost of inference, uncompressed training still consumes excessive hardware resources, run-time and energy. It is highly desirable to directly train a compact low-rank tensorized model from scratch with a low memory and computational cost. However, this is a very challenging task because it is hard to determine a proper tensor rank a priori, which controls the model complexity and compression ratio in the training process. This paper presents a novel end-to-end framework for low-rank tensorized training of neural networks. We first develop a flexible Bayesian model that can handle various low-rank tensor formats (e.g., CP, Tucker, tensor train and tensor-train matrix) that compress neural network parameters in training. This model can automatically determine the tensor ranks inside a nonlinear forward model, which is beyond the capability of existing Bayesian tensor methods. We further develop a scalable stochastic variational inference solver to estimate the posterior density of large-scale problems in training. Our work provides the first general-purpose rank-adaptive framework for end-to-end tensorized training. Our numerical results on various neural network architectures show orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the training process.

Canonical correlation analysis is a statistical technique -dating back at least to [1] - that is used to maximally correlate multiple datasets for joint analysis. The technique has become a fundamental tool in biomedical research where technological advances have led to a huge number of multi-omic datasets ([2]; [3]; [4]). Over the past two decades, limited sample sizes, growing dimensionality, and the search for meaningful biological interpretations, have led to the development of sparse canonical correlation analysis ([2]), where a sparsity assumption is imposed on the canonical correlation vectors. This work falls under the topic of the Bayesian estimation of sparse canonical corrlation vectors. Model-based approaches to canonical correlation analysis were developed in the mid 2000's (see e.g., [5]), and paved the way for a Bayesian treatment of canonical correlation analysis ([6];[7]) and sparse canonical correlation analysis ([8]). However an serious shortcoming of such a Bayesian treatment is that this approach naturally requires a complete specification of the joint distribution of the data, so as to specify the likelihood function. This requirement is a serious limitation in many applications, where the data generating process is poorly understood, for example, image data.

Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to endow the parameters of the network with a prior distribution that is meaningful when lifted into the output space of the network. A possible solution is proposed that enables the user to posit an appropriate covariance function for the task at hand. Our approach constructs a prior distribution for the parameters of the network, called a ridgelet prior, that approximates the posited covariance structure in the output space of the network. The approach is rooted in the ridgelet transform and we establish both finite-sample-size error bounds and the consistency of the approximation of the covariance function in a limit where the number of hidden units is increased. Our experimental assessment is limited to a proof-of-concept, where we demonstrate that the ridgelet prior can out-perform an unstructured prior on regression problems for which an informative covariance function can be a priori provided.