PGMax is an open-source Python package for easy specification of discrete Probabilistic Graphical Models (PGMs) as factor graphs, and automatic derivation of efficient and scalable loopy belief propagation (LBP) implementation in JAX. It supports general factor graphs, and can effectively leverage modern accelerators like GPUs for inference. Compared with existing alternatives, PGMax obtains higher-quality inference results with orders-of-magnitude inference speedups. PGMax additionally interacts seamlessly with the rapidly growing JAX ecosystem, opening up exciting new possibilities. Our source code, examples and documentation are available at https://github.com/vicariousinc/PGMax.

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a serious downside for kernel-based models is the high computational cost; given a dataset of $n$ samples, the cost grows as $\mathcal{O}(n^3)$. Existing sparse approximation methods can yield a significant reduction in the computational cost, effectively reducing the real world cost down to as low as $\mathcal{O}(n)$ in certain cases. Despite this remarkable empirical success, significant gaps remain in the existing results for the analytical confidence bounds on the error due to approximation. In this work, we provide novel confidence intervals for the Nystr\"om method and the sparse variational Gaussian processes approximation method. Our confidence intervals lead to improved error bounds in both regression and optimization. We establish these confidence intervals using novel interpretations of the approximate (surrogate) posterior variance of the models.

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods for deep neural networks, building on both the variational Bayesian and Markov chain Monte Carlo (MCMC) frameworks. A fundamental issue with MCMC methods is that the improvements they enable are obtained at the expense of increased computation time and model storage costs. In this paper, we investigate the potential of sparse network structures to flexibly trade-off model storage costs and inference run time against predictive performance and uncertainty quantification ability. We use stochastic gradient MCMC methods as the core Bayesian inference method and consider a variety of approaches for selecting sparse network structures. Surprisingly, our results show that certain classes of randomly selected substructures can perform as well as substructures derived from state-of-the-art iterative pruning methods while drastically reducing model training times.

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from rescaling low-resolution climate models. We propose a statistical approach, called NN-GPR, using Gaussian process regression (GPR) with an infinitely wide deep neural network based covariance function. NN-GPR requires no assumptions about the relationships between models, no interpolation to a common grid, no stationarity assumptions, and automatically downscales as part of its prediction algorithm. Model experiments show that NN-GPR can be highly skillful at surface temperature and precipitation forecasting by preserving geospatial signals at multiple scales and capturing inter-annual variability. Our projections particularly show improved accuracy and uncertainty quantification skill in regions of high variability, which allows us to cheaply assess tail behavior at a 0.44$^\circ$/50 km spatial resolution without a regional climate model (RCM). Evaluations on reanalysis data and SSP245 forced climate models show that NN-GPR produces similar, overall climatologies to the model ensemble while better capturing fine scale spatial patterns. Finally, we compare NN-GPR's regional predictions against two RCMs and show that NN-GPR can rival the performance of RCMs using only global model data as input.

We propose a simple and scalable approach to causal representation learning for multitask learning. Our approach requires minimal modification to existing ML systems, and improves robustness to prior probability shift. The improvement comes from mitigating unobserved confounders that cause the targets, but not the input. We refer to them as target-causing confounders. These confounders induce spurious dependencies between the input and targets. This poses a problem for the conventional approach to multitask learning, due to its assumption that the targets are conditionally independent given the input. Our proposed approach takes into account the dependency between the targets in order to alleviate target-causing confounding. All that is required in addition to usual practice is to estimate the joint distribution of the targets to switch from discriminative to generative classification, and to predict all targets jointly. Our results on the Attributes of People and Taskonomy datasets reflect the conceptual improvement in robustness to prior probability shift.

In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We propose a novel weak supervision algorithm that processes noisy labels, i.e., weak signals, while also considering features of the training data to produce accurate labels for training. Our method searches over classifiers of the data representation to find plausible labelings. We call this paradigm data consistent weak supervision. A key facet of our framework is that we are able to estimate labels for data examples low or no coverage from the weak supervision. In addition, we make no assumptions about the joint distribution of the weak signals and true labels of the data. Instead, we use weak signals and the data features to solve a constrained optimization that enforces data consistency among the labels we generate. Empirical evaluation of our method on different datasets shows that it significantly outperforms state-of-the-art weak supervision methods on both text and image classification tasks.

Online learning via Bayes' theorem allows new data to be continuously integrated into an agent's current beliefs. However, a naive application of Bayesian methods in non stationary environments leads to slow adaptation and results in state estimates that may converge confidently to the wrong parameter value. A common solution when learning in changing environments is to discard/downweight past data; however, this simple mechanism of "forgetting" fails to account for the fact that many real-world environments involve revisiting similar states. We propose a new framework, Bayes with Adaptive Memory (BAM), that takes advantage of past experience by allowing the agent to choose which past observations to remember and which to forget. We demonstrate that BAM generalizes many popular Bayesian update rules for non-stationary environments. Through a variety of experiments, we demonstrate the ability of BAM to continuously adapt in an ever-changing world.

Deep generative models for approximating complicated and often high-dimensional probability distributions became a rapidly developing research field. Normalizing flows are a popular subclass of these generative models. They can be used to model a target distribution by a simpler latent distribution which is usually the standard normal distribution. In this paper, we are interested in finite normalizing flows which are basically concatenations of learned diffeomorphisms. The parameters of the diffeomorphism are adapted to the target distribution by minimizing a loss functions. To this end, the diffeomorphism must have a tractable Jacobian determinant. For the continuous counterpart of normalizing flows, we refer to the overview paper [43] and the references therein. Suitable architectures of finite normalizing flows include invertible residual neural networks (ResNets) [7, 11, 22], (coupling-based) invertible neural networks (INNs) [4, 14, 29, 34, 40] and autoregessive flows [13, 15, 26, 38].

Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit various types of inference to be performed in linear-time and a feed-forward fashion like neural networks. In more recent years, the role of tractable circuits has significantly expanded as they became a computational and semantical backbone for some approaches that aim to integrate knowledge, reasoning and learning. In this article, we review the foundations of tractable circuits and some associated milestones, while focusing on their core properties and techniques that make them particularly useful for the broad aims of neuro-symbolic AI.

This paper presents a comprehensive review of methods covering significant subjective and objective human stress detection techniques available in the literature. The methods for measuring human stress responses could include subjective questionnaires (developed by psychologists) and objective markers observed using data from wearable and non-wearable sensors. In particular, wearable sensor-based methods commonly use data from electroencephalography, electrocardiogram, galvanic skin response, electromyography, electrodermal activity, heart rate, heart rate variability, and photoplethysmography both individually and in multimodal fusion strategies. Whereas, methods based on non-wearable sensors include strategies such as analyzing pupil dilation and speech, smartphone data, eye movement, body posture, and thermal imaging. Whenever a stressful situation is encountered by an individual, physiological, physical, or behavioral changes are induced which help in coping with the challenge at hand. A wide range of studies has attempted to establish a relationship between these stressful situations and the response of human beings by using different kinds of psychological, physiological, physical, and behavioral measures. Inspired by the lack of availability of a definitive verdict about the relationship of human stress with these different kinds of markers, a detailed survey about human stress detection methods is conducted in this paper. In particular, we explore how stress detection methods can benefit from artificial intelligence utilizing relevant data from various sources. This review will prove to be a reference document that would provide guidelines for future research enabling effective detection of human stress conditions.