This paper presents a computationally efficient and distributed speaker diarization framework for networked IoT-style audio devices. The work proposes a Federated Learning model which can identify the participants in a conversation without the requirement of a large audio database for training. An unsupervised online update mechanism is proposed for the Federated Learning model which depends on cosine similarity of speaker embeddings. Moreover, the proposed diarization system solves the problem of speaker change detection via. unsupervised segmentation techniques using Hotelling's t-squared Statistic and Bayesian Information Criterion. In this new approach, speaker change detection is biased around detected quasi-silences, which reduces the severity of the trade-off between the missed detection and false detection rates. Additionally, the computational overhead due to frame-by-frame identification of speakers is reduced via. unsupervised clustering of speech segments. The results demonstrate the effectiveness of the proposed training method in the presence of non-IID speech data. It also shows a considerable improvement in the reduction of false and missed detection at the segmentation stage, while reducing the computational overhead. Improved accuracy and reduced computational cost makes the mechanism suitable for real-time speaker diarization across a distributed IoT audio network.

In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance test. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past trials and errors. We apply recursive partitioning classifiers on the ABC lookup table to sequentially refine high-likelihood regions into boxes. Each box is regarded as an arm in a binary bandit problem treating ABC acceptance as a reward. Each arm has a proclivity for being chosen for the next ABC evaluation, depending on the prior distribution and past rejections. The method places more splits in those areas where the likelihood resides, shying away from low-probability regions destined for ABC rejections. We provide two versions: (1) ABC-Tree for posterior sampling, and (2) ABC-MAP for maximum a posteriori estimation. We demonstrate accurate ABC approximability at much lower simulation cost. We justify the use of our tree-based bandit algorithms with nearly optimal regret bounds. Finally, we successfully apply our approach to the problem of masked image classification using deep generative models.

The growing capabilities of AI raise questions about their trustworthiness in healthcare, particularly due to opaque decision-making and limited data availability. This paper proposes a novel approach to address these challenges, introducing a Bayesian Monte Carlo Dropout model with kernel modelling. Our model is designed to enhance reliability on small medical datasets, a crucial barrier to the wider adoption of AI in healthcare. This model leverages existing language models for improved effectiveness and seamlessly integrates with current workflows. We demonstrate significant improvements in reliability, even with limited data, offering a promising step towards building trust in AI-driven medical predictions and unlocking its potential to improve patient care.

We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level $\zeta$. At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes. Specifically, we demonstrate that for an MDP characterized by a minimal suboptimality gap $\Delta$, Cert-LSVI-UCB has a cumulative regret of $\tilde{\mathcal{O}}(d^3H^5/\Delta)$ with high probability, provided that the misspecification level $\zeta$ is below $\tilde{\mathcal{O}}(\Delta / (\sqrt{d}H^2))$. Remarkably, this regret bound remains constant relative to the number of episodes $K$. To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation for infinite runs without relying on prior distribution assumptions. This not only highlights the robustness of Cert-LSVI-UCB to model misspecification but also introduces novel algorithmic designs and analytical techniques of independent interest.

Clinical data informs the personalization of health care with a potential for more effective disease management. In practice, this is achieved by subgrouping, whereby clusters with similar patient characteristics are identified and then receive customized treatment plans with the goal of targeting subgroup-specific disease dynamics. In this paper, we propose a novel mixture hidden Markov model for subgrouping patient trajectories from chronic diseases. Our model is probabilistic and carefully designed to capture different trajectory phases of chronic diseases (i.e., "severe", "moderate", and "mild") through tailored latent states. We demonstrate our subgrouping framework based on a longitudinal study across 847 patients with non-specific low back pain. Here, our subgrouping framework identifies 8 subgroups. Further, we show that our subgrouping framework outperforms common baselines in terms of cluster validity indices. Finally, we discuss the applicability of the model to other chronic and long-lasting diseases.

Learning from human feedback plays an important role in aligning generative models, such as large language models (LLM). However, the effectiveness of this approach can be influenced by adversaries, who may intentionally provide misleading preferences to manipulate the output in an undesirable or harmful direction. To tackle this challenge, we study a specific model within this problem domain--contextual dueling bandits with adversarial feedback, where the true preference label can be flipped by an adversary. We propose an algorithm namely robust contextual dueling bandit (\algo), which is based on uncertainty-weighted maximum likelihood estimation. Our algorithm achieves an $\tilde O(d\sqrt{T}+dC)$ regret bound, where $T$ is the number of rounds, $d$ is the dimension of the context, and $ 0 \le C \le T$ is the total number of adversarial feedback. We also prove a lower bound to show that our regret bound is nearly optimal, both in scenarios with and without ($C=0$) adversarial feedback. Additionally, we conduct experiments to evaluate our proposed algorithm against various types of adversarial feedback. Experimental results demonstrate its superiority over the state-of-the-art dueling bandit algorithms in the presence of adversarial feedback.

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high-dimensional settings. In this paper, we propose a framework for Bayesian posterior estimation by mapping data to posteriors of parameters using a neural network trained on data simulated from the complex model. Posterior distributions of model parameters are efficiently obtained by feeding observed data into the trained neural network. We show theoretically that our posteriors converge to the true posteriors in Kullback-Leibler divergence. Our approach yields computationally efficient and theoretically justified uncertainty quantification, which is lacking in existing simulation-based neural network approaches. Comprehensive simulation studies highlight our method's robustness and accuracy.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

We propose an analytical solution for approximating the gradient of the Evidence Lower Bound (ELBO) in variational inference problems where the statistical model is a Bayesian network consisting of observations drawn from a mixture of a Gaussian distribution embedded in unrelated clutter, known as the clutter problem. The method employs the reparameterization trick to move the gradient operator inside the expectation and relies on the assumption that, because the likelihood factorizes over the observed data, the variational distribution is generally more compactly supported than the Gaussian distribution in the likelihood factors. This allows efficient local approximation of the individual likelihood factors, which leads to an analytical solution for the integral defining the gradient expectation. We integrate the proposed gradient approximation as the expectation step in an EM (Expectation Maximization) algorithm for maximizing ELBO and test against classical deterministic approaches in Bayesian inference, such as the Laplace approximation, Expectation Propagation and Mean-Field Variational Inference. The proposed method demonstrates good accuracy and rate of convergence together with linear computational complexity.

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the dependence is downweighted by the regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and how it affects computational considerations, providing a rough characterization of the statistical-computational trade-off in $\Xi$-VI. We also investigate the frequentist properties of $\Xi$-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for achieving polynomial-time approximate inference using the method. Finally, we demonstrate the practical advantage of $\Xi$-VI over mean-field variational inference on simulated and real data.