This study investigates the use of Visually Grounded Speech (VGS) models for keyword localisation in speech. The study focusses on two main research questions: (1) Is keyword localisation possible with VGS models and (2) Can keyword localisation be done cross-lingually in a real low-resource setting? Four methods for localisation are proposed and evaluated on an English dataset, with the best-performing method achieving an accuracy of 57%. A new dataset containing spoken captions in Yoruba language is also collected and released for cross-lingual keyword localisation. The cross-lingual model obtains a precision of 16% in actual keyword localisation and this performance can be improved by initialising from a model pretrained on English data. The study presents a detailed analysis of the model's success and failure modes and highlights the challenges of using VGS models for keyword localisation in low-resource settings.

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop sample complexity bounds for the estimator and establish conditions for minimaxity. Our statistical bounds depend on the logging policy through its mixing properties. We show that achieving a particular statistical risk bound involves a subtle and interesting trade-off between the strength of the mixing properties and the number of samples. We demonstrate the validity of our results under various examples, such as ergodic Markov chains, weakly ergodic inhomogeneous Markov chains, and controlled Markov chains with non-stationary Markov, episodic, and greedy controls. Lastly, we use these sample complexity bounds to establish concomitant ones for offline evaluation of stationary Markov control policies.

Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyv\"arinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.

We introduce the Blackwell discount factor for Markov Decision Processes (MDPs). Classical objectives for MDPs include discounted, average, and Blackwell optimality. Many existing approaches to computing average-optimal policies solve for discounted optimal policies with a discount factor close to $1$, but they only work under strong or hard-to-verify assumptions such as ergodicity or weakly communicating MDPs. In this paper, we show that when the discount factor is larger than the Blackwell discount factor $\gamma_{\mathrm{bw}}$, all discounted optimal policies become Blackwell- and average-optimal, and we derive a general upper bound on $\gamma_{\mathrm{bw}}$. The upper bound on $\gamma_{\mathrm{bw}}$ provides the first reduction from average and Blackwell optimality to discounted optimality, without any assumptions, and new polynomial-time algorithms for average- and Blackwell-optimal policies. Our work brings new ideas from the study of polynomials and algebraic numbers to the analysis of MDPs. Our results also apply to robust MDPs, enabling the first algorithms to compute robust Blackwell-optimal policies.

Sparseness and robustness are two important properties for many machine learning scenarios. In the present study, regarding the maximum correntropy criterion (MCC) based robust regression algorithm, we investigate to integrate the MCC method with the automatic relevance determination (ARD) technique in a Bayesian framework, so that MCC-based robust regression could be implemented with adaptive sparseness. To be specific, we use an inherent noise assumption from the MCC to derive an explicit likelihood function, and realize the maximum a posteriori (MAP) estimation with the ARD prior by variational Bayesian inference. Compared to the existing robust and sparse L1-regularized MCC regression, the proposed MCC-ARD regression can eradicate the troublesome tuning for the regularization hyper-parameter which controls the regularization strength. Further, MCC-ARD achieves superior prediction performance and feature selection capability than L1-regularized MCC, as demonstrated by a noisy and high-dimensional simulation study.

The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear as a suitable remedy conveying the predictive ability of ML methods with the probabilistically-oriented practice of econometric research. By adopting a state-of-the-art second-order optimization algorithm, we train a Bayesian bilinear neural network with temporal attention, suitable for the challenging time-series task of predicting mid-price movements in ultra-high-frequency limit-order book markets. We thoroughly compare our Bayesian model with traditional ML alternatives by addressing the use of predictive distributions to analyze errors and uncertainties associated with the estimated parameters and model forecasts. Our results underline the feasibility of the Bayesian deep-learning approach and its predictive and decisional advantages in complex econometric tasks, prompting future research in this direction.

Voice synthesis has seen significant improvements in the past decade resulting in highly intelligible voices. Further investigations have resulted in models that can produce variable speech, including conditional emotional expression. The problem lies, however, in a focus on phrase-level modifications and prosodic vocal features. Using the CREMA-D dataset we have trained a GAN conditioned on emotion to generate worth lengths for a given input text. These word lengths are relative to neutral speech and can be provided, through speech synthesis markup language (SSML) to a text-to-speech (TTS) system to generate more expressive speech. Additionally, a generative model is also trained using implicit maximum likelihood estimation (IMLE) and a comparative analysis with GANs is included. We were able to achieve better performances on objective measures for neutral speech, and better time alignment for happy speech when compared to an out-of-box model. However, further investigation of subjective evaluation is required.

Computational models have become a powerful tool in the quantitative sciences to understand the behaviour of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot be obtained from theory but need to be inferred from data. This is especially the case for models in the social sciences, economics, or computational epidemiology. Yet many current parameter estimation methods are mathematically involved and computationally slow to run. In this paper we present a computationally simple and fast method to retrieve accurate probability densities for model parameters using neural differential equations. We present a pipeline comprising multi-agent models acting as forward solvers for systems of ordinary or stochastic differential equations, and a neural network to then extract parameters from the data generated by the model. The two combined create a powerful tool that can quickly estimate densities on model parameters, even for very large systems. We demonstrate the method on synthetic time series data of the SIR model of the spread of infection, and perform an in-depth analysis of the Harris-Wilson model of economic activity on a network, representing a non-convex problem. For the latter, we apply our method both to synthetic data and to data of economic activity across Greater London. We find that our method calibrates the model orders of magnitude more accurately than a previous study of the same dataset using classical techniques, while running between 195 and 390 times faster.

Estimating an individual's potential outcomes under counterfactual treatments is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, impulse responses, human faces) and covariates are relatively limited. In this case, to construct one's outcome under a counterfactual treatment, it is crucial to leverage individual information contained in its observed factual outcome on top of the covariates. We propose a deep variational Bayesian framework that rigorously integrates two main sources of information for outcome construction under a counterfactual treatment: one source is the individual features embedded in the high-dimensional factual outcome; the other source is the response distribution of similar subjects (subjects with the same covariates) that factually received this treatment of interest.

Molecular dynamics aims at simulating the physical movement of atoms in order to sample the Boltzmann-Gibbs probability measure and the associated trajectories, and to compute macroscopic properties using Monte Carlo estimates [17, 1]. One of the main difficulties when performing these numerical simulations is metastability: the system tends to stay trapped in some regions of the phase space, typically in the vicinity of local maxima of the target probability measure. In this context, transitions from one metastable state to another one are of particular interest in complex systems, as they characterize for example crystallisation or enzymatic reactions. These reactions happen on a long time scale compared to the molecular timescale, so that the simulation of realistic rare events is computationally difficult. On the one hand, many efforts have been devoted to the development of rare events sampling methods in molecular dynamics. The goal of these methods is to characterize transition paths and to compute associated transition rates and mean transition times; see for instance [21] for a review. The most notable methods can be classified in two groups: (i) importance sampling techniques, where the dynamics is biased (by modifying the potential for instance) to reduce the variance of Monte Carlo estimators when computing expectations, see for instance [16, 8] for more details, and also [31, Section 6.2]. It is possible to use adaptive importance sampling strategies to choose the importance function, see [30, Chapter 5]. Another viewpoint is offered by the framework of stochastic control, as in [21] where the modification in the drift of the dynamics is determined by the solution of an optimal control problem.