We introduce SABRE, a novel framework for robust variational Bayesian peer-to-peer federated learning. We analyze the robustness of the known variational Bayesian peer-to-peer federated learning framework (BayP2PFL) against poisoning attacks and subsequently show that BayP2PFL is not robust against those attacks. The new SABRE aggregation methodology is then devised to overcome the limitations of the existing frameworks. SABRE works well in non-IID settings, does not require the majority of the benign nodes over the compromised ones, and even outperforms the baseline algorithm in benign settings. We theoretically prove the robustness of our algorithm against data / model poisoning attacks in a decentralized linear regression setting. Proof-of-Concept evaluations on benchmark data from image classification demonstrate the superiority of SABRE over the existing frameworks under various poisoning attacks.

Change-of-variables (CoV) formulas allow to reduce complicated probability densities to simpler ones by a learned transformation with tractable Jacobian determinant. They are thus powerful tools for maximum-likelihood learning, Bayesian inference, outlier detection, model selection, etc. CoV formulas have been derived for a large variety of model types, but this information is scattered over many separate works. We present a systematic treatment from the unifying perspective of encoder/decoder architectures, which collects 28 CoV formulas in a single place, reveals interesting relationships between seemingly diverse methods, emphasizes important distinctions that are not always clear in the literature, and identifies surprising gaps for future research.

We investigate the problem of estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model (GGM) on the network. In this vein, we consider GGMs whose covariance structures align with the geometry of the weighted network on which they are based. Such GGMs have been of longstanding interest in statistical physics, and are referred to as the Gaussian Free Field (GFF). In recent years, they have attracted considerable interest in the machine learning and theoretical computer science. In this work, we propose a novel estimator for the weighted network (equivalently, its Laplacian) from repeated measurements of a GFF on the network, based on the Fourier analytic properties of the Gaussian distribution. In this pursuit, our approach exploits complex-valued statistics constructed from observed data, that are of interest on their own right. We demonstrate the effectiveness of our estimator with concrete recovery guarantees and bounds on the required sample complexity. In particular, we show that the proposed statistic achieves the parametric rate of estimation for fixed network size. In the setting of networks growing with sample size, our results show that for Erdos-Renyi random graphs $G(d,p)$ above the connectivity threshold, we demonstrate that network recovery takes place with high probability as soon as the sample size $n$ satisfies $n \gg d^4 \log d \cdot p^{-2}$.

This paper introduces a first implementation of a novel likelihood-ratio-based approach for constructing confidence intervals for neural networks. Our method, called DeepLR, offers several qualitative advantages: most notably, the ability to construct asymmetric intervals that expand in regions with a limited amount of data, and the inherent incorporation of factors such as the amount of training time, network architecture, and regularization techniques. While acknowledging that the current implementation of the method is prohibitively expensive for many deep-learning applications, the high cost may already be justified in specific fields like medical predictions or astrophysics, where a reliable uncertainty estimate for a single prediction is essential. This work highlights the significant potential of a likelihood-ratio-based uncertainty estimate and establishes a promising avenue for future research.

This article aims to investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we propose algorithms and methods that can effectively distinguish between thermal and multiplicative noise and improve the precision of parameter estimation for optimal data analysis. Specifically, we explore the impact of both multiplicative and thermal noise on the obfuscation of the actual signal and propose methods to resolve them. Firstly, we present an algorithm that can effectively separate thermal noise with comparable performance to Hamilton Monte Carlo (HMC) but with significantly improved speed. Subsequently, we analyze multiplicative noise and demonstrate that HMC is insufficient for isolating thermal and multiplicative noise. However, we show that, with additional knowledge of the ratio between thermal and multiplicative noise, we can accurately distinguish between the two types of noise when provided with a sufficiently large sampling rate or an amplitude of multiplicative noise smaller than thermal noise. This finding results in a situation that initially seems counterintuitive. When multiplicative noise dominates the noise spectrum, we can successfully estimate the parameters for such systems after adding additional white noise to shift the noise balance.

We introduce the problem of phone classification in the context of speech recognition, and explore several sets of local spectro-temporal features that can be used for phone classification. In particular, we present some preliminary results for phone classification using two sets of features that are commonly used for object detection: Haar features and SVM-classified Histograms of Gradients (HoG).

Chandola et al (2009) subdivided anomalies into three types: point anomalies (an object is considered anomalous when compared against the rest of objects), contextual anomalies (an object is anomalous in a specific context), and collective anomalies (a collection of objects is anomalous with respect to the entire dataset). The analysis of anomalies has a wide range of applications, such as in network security (Ahmed et al, 2016a), bioinformatics (Spinosa and Carvalho, 2005), fraud detection (Ahmed et al, 2016b), and fault detection and isolation (Hwang et al, 2009). Anomaly analysis consists of two equally important tasks: anomaly detection and anomaly explanation. A wealth of'shallow' machine learning based methods, i.e., not based on deep learning, have been proposed to detect anomalies (Chandola et al, 2009). More recently, many deep learning based anomaly detection methods have also been developed (Pang et al, 2021). However, deep learning based anomaly detection methods are notoriously known as not being interpretable, in the sense that generally both the model itself is non-transparent and the resulting anomaly scores are challenging to interpret without the use of a post-hoc explainer.

Disordered many-body systems exhibit a wide range of emergent phenomena across different scales. These complex behaviors can be utilized for various information processing tasks such as error correction, learning, and optimization. Despite the empirical success of utilizing these systems for intelligent tasks, the underlying principles that govern their emergent intelligent behaviors remain largely unknown. In this thesis, we aim to characterize such emergent intelligence in disordered systems through statistical physics. We chart a roadmap for our efforts in this thesis based on two axes: learning mechanisms (long-term memory vs. working memory) and learning dynamics (artificial vs. natural). Throughout our journey, we uncover relationships between learning mechanisms and physical dynamics that could serve as guiding principles for designing intelligent systems. We hope that our investigation into the emergent intelligence of seemingly disparate learning systems can expand our current understanding of intelligence beyond neural systems and uncover a wider range of computational substrates suitable for AI applications.

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex data transformations. In this study, we explore the use of quaternions to represent and classify rotation data, using randomly generated quaternion data and corresponding labels, converting quaternions to rotation matrices, and using them as input features. Based on quaternions and multiple machine learning algorithms, it has shown higher accuracy and significantly improved performance in prediction tasks. Overall, this study provides an empirical basis for exploiting quaternions for machine learning tasks.

Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes that produce varying amounts of information about the underlying uncertain parameters of the system. To maximize information gained with respect to these uncertain parameters we present a Bayesian approach to data collection for system identification called Bayesian Optimal Experimental Design (BOED). The formulation uses parameterized trajectories and cubature to compute maximally informative system trajectories which obtain as much information as possible about unknown system parameters while also ensuring safety under mild assumptions. The proposed method is applicable to non-linear and non-Gaussian systems and is applied to a high-fidelity vehicle model from the literature. It is shown the proposed approach requires orders of magnitude fewer samples compared to state-of-the-art BOED algorithms from the literature while simultaneously providing safety guarantees.