Vertical federated learning (VFL) has emerged as a paradigm for collaborative model estimation across multiple clients, each holding a distinct set of covariates. This paper introduces the first comprehensive framework for fitting Bayesian models in the VFL setting. We propose a novel approach that leverages data augmentation techniques to transform VFL problems into a form compatible with existing Bayesian federated learning algorithms. We present an innovative model formulation for specific VFL scenarios where the joint likelihood factorizes into a product of client-specific likelihoods. To mitigate the dimensionality challenge posed by data augmentation, which scales with the number of observations and clients, we develop a factorized amortized variational approximation that achieves scalability independent of the number of observations. We showcase the efficacy of our framework through extensive numerical experiments on logistic regression, multilevel regression, and a novel hierarchical Bayesian split neural net model. Our work paves the way for privacy-preserving, decentralized Bayesian inference in vertically partitioned data scenarios, opening up new avenues for research and applications in various domains.

Artificial intelligence (AI) has made significant advances in recent years and opened up new possibilities in exploring applications in various fields such as biomedical, robotics, education, industry, etc. Among these fields, human hand gesture recognition is a subject of study that has recently emerged as a research interest in robotic hand control using electromyography (EMG). Surface electromyography (sEMG) is a primary technique used in EMG, which is popular due to its non-invasive nature and is used to capture gesture movements using signal acquisition devices placed on the surface of the forearm. Moreover, these signals are pre-processed to extract significant handcrafted features through time and frequency domain analysis. These are helpful and act as input to machine learning (ML) models to identify hand gestures. However, handling multiple classes and biases are major limitations that can affect the performance of an ML model. Therefore, to address this issue, a new mixture of experts extra tree (MEET) model is proposed to identify more accurate and effective hand gesture movements. This model combines individual ML models referred to as experts, each focusing on a minimal class of two. Moreover, a fully trained model known as the gate is employed to weigh the output of individual expert models. This amalgamation of the expert models with the gate model is known as a mixture of experts extra tree (MEET) model. In this study, four subjects with six hand gesture movements have been considered and their identification is evaluated among eleven models, including the MEET classifier. Results elucidate that the MEET classifier performed best among other algorithms and identified hand gesture movement accurately.

Drug discovery is a complex process that involves sequentially screening and examining a vast array of molecules to identify those with the target properties. This process, also referred to as sequential experimentation, faces challenges due to the vast search space, the rarity of target molecules, and constraints imposed by limited data and experimental budgets. To address these challenges, we introduce a human-in-the-loop framework for sequential experiments in drug discovery. This collaborative approach combines human expert knowledge with deep learning algorithms, enhancing the discovery of target molecules within a specified experimental budget. The proposed algorithm processes experimental data to recommend both promising molecules and those that could improve its performance to human experts. Human experts retain the final decision-making authority based on these recommendations and their domain expertise, including the ability to override algorithmic recommendations. We applied our method to drug discovery tasks using real-world data and found that it consistently outperforms all baseline methods, including those which rely solely on human or algorithmic input. This demonstrates the complementarity between human experts and the algorithm. Our results provide key insights into the levels of humans' domain knowledge, the importance of meta-knowledge, and effective work delegation strategies. Our findings suggest that such a framework can significantly accelerate the development of new vaccines and drugs by leveraging the best of both human and artificial intelligence.

Uncertainty has long been a critical area of study in robotics, particularly when robots are equipped with analytical models. As we move towards the widespread use of deep neural networks in robots, which have demonstrated remarkable performance in research settings, understanding the nuances of uncertainty becomes crucial for their real-world deployment. This guide offers an overview of the importance of uncertainty and provides methods to quantify and evaluate it from an applications perspective.

Fine-tuned Large Language Models (LLMs) often suffer from overconfidence and poor calibration, particularly when fine-tuned on small datasets. To address these challenges, we propose a simple combination of Low-Rank Adaptation (LoRA) with Gaussian Stochastic Weight Averaging (SWAG), facilitating approximate Bayesian inference in LLMs. Through extensive testing across several Natural Language Processing (NLP) benchmarks, we demonstrate that our straightforward and computationally efficient approach improves model generalization and calibration competitively with comparable, more sophisticated methods for Bayesian inference in LLMs. We further show that our method exhibits greater robustness against distribution shift, as reflected in its performance on out-of-distribution tasks.

Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples suffers from an optimization and an approximation curse of dimensionality. It may be avoided by following a hierarchic probability flow from coarse to fine scales. This inverse renormalization group is defined by conditional probabilities across scales, renormalized in a wavelet basis. For a $\varphi^4$ scalar potential, sampling these hierarchic models avoids the critical slowing down at the phase transition. An outstanding issue is to also approximate non-Gaussian fields having long-range interactions in space and across scales. We introduce low-dimensional models with robust multiscale approximations of high order polynomial energies. They are calculated with a second wavelet transform, which defines interactions over two hierarchies of scales. We estimate and sample these wavelet scattering models to generate 2D vorticity fields of turbulence, and images of dark matter densities.

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.

Inspired by the human cognitive system, attention is a mechanism that imitates the human cognitive awareness about specific information, amplifying critical details to focus more on the essential aspects of data. Deep learning has employed attention to boost performance for many applications. Interestingly, the same attention design can suit processing different data modalities and can easily be incorporated into large networks. Furthermore, multiple complementary attention mechanisms can be incorporated into one network. Hence, attention techniques have become extremely attractive. However, the literature lacks a comprehensive survey on attention techniques to guide researchers in employing attention in their deep models. Note that, besides being demanding in terms of training data and computational resources, transformers only cover a single category in self-attention out of the many categories available. We fill this gap and provide an in-depth survey of 50 attention techniques, categorizing them by their most prominent features. We initiate our discussion by introducing the fundamental concepts behind the success of the attention mechanism. Next, we furnish some essentials such as the strengths and limitations of each attention category, describe their fundamental building blocks, basic formulations with primary usage, and applications specifically for computer vision. We also discuss the challenges and general open questions related to attention mechanisms. Finally, we recommend possible future research directions for deep attention. All the information about visual attention methods in deep learning is provided at \href{https://github.com/saeed-anwar/VisualAttention}{https://github.com/saeed-anwar/VisualAttention}

Abstract-- We introduce an advanced, swift pattern recognition strategy for various multiple robotics during curve negotiation. Initially, the paradigm considers robot locations and features as quintessential parameters indicative of divergent robot patterns. The utilization of and underpins the foundational control mechanisms stochastic process theories, particularly the Hidden Markov for sophisticated robot dynamics technologies [1], [2], [3], Model--a form of dynamic Bayesian network--has proven [4], the accurate identification and forecasting of robot's instrumental in elucidating the intricate correlations between group motion and distribution emerge as critical undertakings. Moreover, advanced probabilistic models, including the design of robot dynamics and assistance systems [5], the ARX framework and its stochastic variant [10], the [6]. This necessitates a comprehensive analysis of robotics, SS-ARX model, have been developed to accurately reflect the encompassing both their distribution and feature conditions, unpredictability inherent in robotics status, enabling refined as well as their status patterns (identifiable as functional classification and prediction of robotics distribution.

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential nonlinear relationships among the variables. To address this limitation, we propose a partially linear structure that incorporates unspecified functions to capture nonlinear relationships. We establish the identifiability of the proposed model under mild conditions and introduce a practical estimation algorithm. We present the performance of our approach through numerical studies, including simulations and real data analysis.