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.

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.

The present work addresses theoretical and practical questions in the domain of Deep Learning for High Frequency Trading. State-of-the-art models such as Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are reviewed and compared on the same tasks, feature space and dataset, and then clustered according to pairwise similarity and performance metrics. The underlying dimensions of the modeling techniques are hence investigated to understand whether these are intrinsic to the Limit Order Book's dynamics. We observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.

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.

Imbalanced learning (IL), i.e., learning unbiased models from class-imbalanced data, is a challenging problem. Typical IL methods including resampling and reweighting were designed based on some heuristic assumptions. They often suffer from unstable performance, poor applicability, and high computational cost in complex tasks where their assumptions do not hold. In this paper, we introduce a novel ensemble IL framework named MESA. It adaptively resamples the training set in iterations to get multiple classifiers and forms a cascade ensemble model. MESA directly learns the sampling strategy from data to optimize the final metric beyond following random heuristics. Moreover, unlike prevailing meta-learning-based IL solutions, we decouple the model-training and meta-training in MESA by independently train the meta-sampler over task-agnostic meta-data. This makes MESA generally applicable to most of the existing learning models and the meta-sampler can be efficiently applied to new tasks. Extensive experiments on both synthetic and real-world tasks demonstrate the effectiveness, robustness, and transferability of MESA. Our code is available at https://github.com/ZhiningLiu1998/mesa.

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.