The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the data likelihood is Gaussian. Moreover, inference for GPLVMs has typically been restricted to obtaining maximum a posteriori point estimates, which can lead to overfitting, or variational approximations, which mischaracterize the posterior uncertainty. Here, we present a method to perform Markov chain Monte Carlo (MCMC) inference for generalized Bayesian nonlinear latent variable modeling. The crucial insight necessary to generalize GPLVMs to arbitrary observation models is that we approximate the kernel function in the Gaussian process mappings with random Fourier features; this allows us to compute the gradient of the posterior in closed form with respect to the latent variables. We show that we can generalize GPLVMs to non-Gaussian observations, such as Poisson, negative binomial, and multinomial distributions, using our random feature latent variable model (RFLVM). Our generalized RFLVMs perform on par with state-of-the-art latent variable models on a wide range of applications, including motion capture, images, and text data for the purpose of estimating the latent structure and imputing the missing data of these complex data sets. Keywords: Latent variable modeling, Gaussian processes, probabilistic modeling.

Objective: Seizure prediction is of great importance to improve the life of patients. The focal point is to distinguish preictal states from interictal ones. With the development of machine learning, seizure prediction methods have achieved significant progress. However, the severe imbalance problem between preictal and interictal data still poses a great challenge, restricting the performance of classifiers. Data augmentation is an intuitive way to solve this problem. Existing data augmentation methods generate samples by overlapping or recombining data. The distribution of generated samples is limited by original data, because such transformations cannot fully explore the feature space and offer new information. As the epileptic EEG representation varies among seizures, these generated samples cannot provide enough diversity to achieve high performance on a new seizure. As a consequence, we propose a novel data augmentation method with diffusion model called DiffEEG. Methods: Diffusion models are a class of generative models that consist of two processes. Specifically, in the diffusion process, the model adds noise to the input EEG sample step by step and converts the noisy sample into output random noise, exploring the distribution of data by minimizing the loss between the output and the noise added. In the denoised process, the model samples the synthetic data by removing the noise gradually, diffusing the data distribution to outward areas and narrowing the distance between different clusters. Results: We compared DiffEEG with existing methods, and integrated them into three representative classifiers. The experiments indicate that DiffEEG could further improve the performance and shows superiority to existing methods. Conclusion: This paper proposes a novel and effective method to solve the imbalanced problem and demonstrates the effectiveness and generality of our method.

We present a novel learning-based method that achieves state-of-the-art performance on several heart rate estimation benchmarks extracted from photoplethysmography signals (PPG). We consider the evolution of the heart rate in the context of a discrete-time stochastic process that we represent as a hidden Markov model. We derive a distribution over possible heart rate values for a given PPG signal window through a trained neural network. Using belief propagation, we incorporate the statistical distribution of heart rate changes to refine these estimates in a temporal context. From this, we obtain a quantized probability distribution over the range of possible heart rate values that captures a meaningful and well-calibrated estimate of the inherent predictive uncertainty. We show the robustness of our method on eight public datasets with three different cross-validation experiments.

An alternative to stratified is parallel integration. In contrast to stratified frameworks, parallel integration applies in settings Parallel neurosymbolic architectures have been in which the same task can be solved both symbolically applied effectively in NLP by distilling knowledge and sub-symbolically and the aim is to increase the accuracy from a logic theory into a deep model. However, of the end task by distilling knowledge from the logic prior art faces several limitations including component into the neural one and vice versa. Two parallel supporting restricted forms of logic theories and neurosymbolic frameworks have been proposed recently: relying on the assumption of independence between Teacher-Student (T-S) by Hu et al. (Hu et al., 2016a;b) and the logic and the deep network.

This survey paper provides a comprehensive review of the use of diffusion models in natural language processing (NLP). Diffusion models are a class of mathematical models that aim to capture the diffusion of information or signals across a network or manifold. In NLP, diffusion models have been used in a variety of applications, such as natural language generation, sentiment analysis, topic modeling, and machine translation. This paper discusses the different formulations of diffusion models used in NLP, their strengths and limitations, and their applications. We also perform a thorough comparison between diffusion models and alternative generative models, specifically highlighting the autoregressive (AR) models, while also examining how diverse architectures incorporate the Transformer in conjunction with diffusion models. Compared to AR models, diffusion models have significant advantages for parallel generation, text interpolation, token-level controls such as syntactic structures and semantic contents, and robustness. Exploring further permutations of integrating Transformers into diffusion models would be a valuable pursuit. Also, the development of multimodal diffusion models and large-scale diffusion language models with notable capabilities for few-shot learning would be important directions for the future advance of diffusion models in NLP.

Many Artificial Intelligence (AI) algorithms are inspired by physics and employ stochastic fluctuations. We connect these physics-inspired AI algorithms by unifying them under a single mathematical framework that we call Thermodynamic AI. Seemingly disparate algorithmic classes can be described by this framework, for example, (1) Generative diffusion models, (2) Bayesian neural networks, (3) Monte Carlo sampling and (4) Simulated annealing. Such Thermodynamic AI algorithms are currently run on digital hardware, ultimately limiting their scalability and overall potential. Stochastic fluctuations naturally occur in physical thermodynamic systems, and such fluctuations can be viewed as a computational resource. Hence, we propose a novel computing paradigm, where software and hardware become inseparable. Our algorithmic unification allows us to identify a single full-stack paradigm, involving Thermodynamic AI hardware, that could accelerate such algorithms. We contrast Thermodynamic AI hardware with quantum computing where noise is a roadblock rather than a resource. Thermodynamic AI hardware can be viewed as a novel form of computing, since it uses a novel fundamental building block. We identify stochastic bits (s-bits) and stochastic modes (s-modes) as the respective building blocks for discrete and continuous Thermodynamic AI hardware. In addition to these stochastic units, Thermodynamic AI hardware employs a Maxwell's demon device that guides the system to produce non-trivial states. We provide a few simple physical architectures for building these devices and we develop a formalism for programming the hardware via gate sequences. We hope to stimulate discussion around this new computing paradigm. Beyond acceleration, we believe it will impact the design of both hardware and algorithms, while also deepening our understanding of the connection between physics and intelligence.

A common challenge in applying graph machine learning methods is that the underlying graph Learning the graph structure underlying a set of smooth signals of a system is often unknown. Although different is a classical problem in GSP. Well-established methods graph inference methods have been proposed optimize a graph representation, usually the graph adjacency for continuous graph signals, inferring the matrix or the graph Laplacian, so that the total variation of graph structure underlying other types of data, given signals will be minimal on the learned graph (Dong such as discrete counts, is under-explored. In et al., 2016; Kalofolias, 2016; Egilmez et al., 2017; Kumar this paper, we generalize a graph signal processing et al., 2020). However, smooth graph signals are rarely (GSP) framework for learning a graph from encountered in the real world and one is often required to smooth graph signals to the exponential family deal with noisy signals.

In several practical applications of federated learning (FL), the clients are highly heterogeneous in terms of both their data and compute resources, and therefore enforcing the same model architecture for each client is very limiting. Moreover, the need for uncertainty quantification and data privacy constraints are often particularly amplified for clients that have limited local data. This paper presents a unified FL framework to simultaneously address all these constraints and concerns, based on training customized local Bayesian models that learn well even in the absence of large local datasets. A Bayesian framework provides a natural way of incorporating supervision in the form of prior distributions. We use priors in the functional (output) space of the networks to facilitate collaboration across heterogeneous clients. Moreover, formal differential privacy guarantees are provided for this framework. Experiments on standard FL datasets demonstrate that our approach outperforms strong baselines in both homogeneous and heterogeneous settings and under strict privacy constraints, while also providing characterizations of model uncertainties.

A polynomial-time exact algorithm for counting the number of directed acyclic graphs in a Markov equivalence class was recently given by Wien\"obst, Bannach, and Li\'skiewicz (AAAI 2021). In this paper, we consider the more general problem of counting the number of directed acyclic graphs in a Markov equivalence class when the directions of some of the edges are also fixed (this setting arises, for example, when interventional data is partially available). This problem has been shown in earlier work to be complexity-theoretically hard. In contrast, we show that the problem is nevertheless tractable in an interesting class of instances, by establishing that it is ``fixed-parameter tractable''. In particular, our counting algorithm runs in time that is bounded by a polynomial in the size of the graph, where the degree of the polynomial does \emph{not} depend upon the number of additional edges provided as input.

Causal structure learning, a prominent technique for encoding cause and effect relationships among variables, through Bayesian Networks (BNs). Merely recovering causal structures from real-world observed data lacks precision, while the development of Large Language Models (LLM) is opening a new frontier of causality. LLM presents strong capability in discovering causal relationships between variables with the "text" inputs defining the investigated variables, leading to a potential new hierarchy and new ladder of causality. We aim an critical issue in the emerging topic of LLM based causal structure learning, to tackle erroneous prior causal statements from LLM, which is seldom considered in the current context of expert dominating prior resources. As a pioneer attempt, we propose a BN learning strategy resilient to prior errors without need of human intervention. Focusing on the edge-level prior, we classify the possible prior errors into three types: order-consistent, order-reversed, and irrelevant, and provide their theoretical impact on the Structural Hamming Distance (SHD) under the presumption of sufficient data. Intriguingly, we discover and prove that only the order-reversed error contributes to an increase in a unique acyclic closed structure, defined as a "quasi-circle". Leveraging this insight, a post-hoc strategy is employed to identify the order-reversed prior error by its impact on the increment of "quasi-circles". Through empirical evaluation on both real and synthetic datasets, we demonstrate our strategy's robustness against prior errors. Specifically, we highlight its substantial ability to resist order-reversed errors while maintaining the majority of correct prior knowledge.