Semi-supervised learning (SSL) is a machine learning methodology that leverages unlabeled data in conjunction with a limited amount of labeled data. Although SSL has been applied in various applications and its effectiveness has been empirically demonstrated, it is still not fully understood when and why SSL performs well. Some existing theoretical studies have attempted to address this issue by modeling classification problems using the so-called Gaussian Mixture Model (GMM). These studies provide notable and insightful interpretations. However, their analyses are focused on specific purposes, and a thorough investigation of the properties of GMM in the context of SSL has been lacking. In this paper, we conduct such a detailed analysis of the properties of the high-dimensional GMM for binary classification in the SSL setting. To this end, we employ the approximate message passing and state evolution methods, which are widely used in high-dimensional settings and originate from statistical mechanics. We deal with two estimation approaches: the Bayesian one and the l2-regularized maximum likelihood estimation (RMLE). We conduct a comprehensive comparison between these two approaches, examining aspects such as the global phase diagram, estimation error for the parameters, and prediction error for the labels. A specific comparison is made between the Bayes-optimal (BO) estimator and RMLE, as the BO setting provides optimal estimation performance and is ideal as a benchmark. Our analysis shows that with appropriate regularizations, RMLE can achieve near-optimal performance in terms of both the estimation error and prediction error, especially when there is a large amount of unlabeled data. These results demonstrate that the l2 regularization term plays an effective role in estimation and prediction in SSL approaches.

The detection of phase transitions is a central task in many-body physics. To automate this process, the task can be phrased as a classification problem. Classification problems can be approached in two fundamentally distinct ways: through either a discriminative or a generative method. In general, it is unclear which of these two approaches is most suitable for a given problem. The choice is expected to depend on factors such as the availability of system knowledge, dataset size, desired accuracy, computational resources, and other considerations. In this work, we answer the question of how one should approach the solution of phase-classification problems by performing a numerical case study on the thermal phase transition in the classical two-dimensional square-lattice ferromagnetic Ising model.

Constructing valid confidence sets is a crucial task in statistical inference, yet traditional methods often face challenges when dealing with complex models or limited observed sample sizes. These challenges are frequently encountered in modern applications, such as Likelihood-Free Inference (LFI). In these settings, confidence sets may fail to maintain a confidence level close to the nominal value. In this paper, we introduce two novel methods, TRUST and TRUST++, for calibrating confidence sets to achieve distribution-free conditional coverage. These methods rely entirely on simulated data from the statistical model to perform calibration. Leveraging insights from conformal prediction techniques adapted to the statistical inference context, our methods ensure both finite-sample local coverage and asymptotic conditional coverage as the number of simulations increases, even if n is small. They effectively handle nuisance parameters and provide computationally efficient uncertainty quantification for the estimated confidence sets. This allows users to assess whether additional simulations are necessary for robust inference. Through theoretical analysis and experiments on models with both tractable and intractable likelihoods, we demonstrate that our methods outperform existing approaches, particularly in small-sample regimes.

The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering techniques. However, in many real-world problems, some (or all) of the uncertainty is epistemic, arising from a lack of knowledge, and is difficult to model probabilistically. This paper introduces a possibilistic ensemble Kalman filter designed for this setting and characterizes some of its properties. Using possibility theory to describe epistemic uncertainty is appealing from a philosophical perspective, and it is easy to justify certain heuristics often employed in standard ensemble Kalman filters as principled approaches to capturing uncertainty within it. The possibilistic approach motivates a robust mechanism for characterizing uncertainty which shows good performance with small sample sizes, and can outperform standard ensemble Kalman filters at given sample size, even when dealing with genuinely aleatoric uncertainty.

Catastrophic forgetting has been the leading issue in the domain of lifelong learning in artificial systems. Current artificial systems are reasonably good at learning domains they have seen before; however, as soon as they encounter something new, they either go through a significant performance deterioration or if you try to teach them the new distribution of data, they forget what they have learned before. Additionally, they are also prone to being overly confident when performing inference on seen as well as unseen data, causing significant reliability issues when lives are at stake. Therefore, it is extremely important to dig into this problem and formulate an approach that will be continually adaptable as well as reliable. If we move away from the engineering domain of such systems and look into biological systems, we can realize that these very systems are very efficient at computing the reliance as well as the uncertainty of accurate predictions that further help them refine the inference in a life-long setting. These systems are not perfect; however, they do give us a solid understanding of the reasoning under uncertainty which takes us to the domain of Bayesian reasoning. We incorporate this Bayesian inference with thresholding mechanism as to mimic more biologically inspired models, but only at spatial level. Further, we reproduce a recent study on Bayesian Inference with Spiking Neural Networks for Continual Learning to compare against it as a suitable biologically inspired Bayesian framework. Overall, we investigate the plausibility of biologically inspired Bayesian Learning in artificial systems on a vision dataset, MNIST, and show relative performance improvement under the conditions when the model is forced to predict VS when the model is not.

As AI systems become increasingly powerful, the need for safe AI has become more pressing. Humans are an attractive model for AI safety: as the only known agents capable of general intelligence, they perform robustly even under conditions that deviate significantly from prior experiences, explore the world safely, understand pragmatics, and can cooperate to meet their intrinsic goals. Intelligence, when coupled with cooperation and safety mechanisms, can drive sustained progress and well-being. These properties are a function of the architecture of the brain and the learning algorithms it implements. Neuroscience may thus hold important keys to technical AI safety that are currently underexplored and underutilized. In this roadmap, we highlight and critically evaluate several paths toward AI safety inspired by neuroscience: emulating the brain's representations, information processing, and architecture; building robust sensory and motor systems from imitating brain data and bodies; fine-tuning AI systems on brain data; advancing interpretability using neuroscience methods; and scaling up cognitively-inspired architectures. We make several concrete recommendations for how neuroscience can positively impact AI safety.

The reliable recovery and uncertainty quantification of a fixed effect function $\mu$ in a functional mixed model, for modelling population- and object-level variability in noisily observed functional data, is a notoriously challenging task: variations along the $x$ and $y$ axes are confounded with additive measurement error, and cannot in general be disentangled. The question then as to what properties of $\mu$ may be reliably recovered becomes important. We demonstrate that it is possible to recover the size-and-shape of a square-integrable $\mu$ under a Bayesian functional mixed model. The size-and-shape of $\mu$ is a geometric property invariant to a family of space-time unitary transformations, viewed as rotations of the Hilbert space, that jointly transform the $x$ and $y$ axes. A random object-level unitary transformation then captures size-and-shape \emph{preserving} deviations of $\mu$ from an individual function, while a random linear term and measurement error capture size-and-shape \emph{altering} deviations. The model is regularized by appropriate priors on the unitary transformations, posterior summaries of which may then be suitably interpreted as optimal data-driven rotations of a fixed orthonormal basis for the Hilbert space. Our numerical experiments demonstrate utility of the proposed model, and superiority over the current state-of-the-art.

Federated Learning (FL) has emerged as a promising method to collaboratively learn from decentralized and heterogeneous data available at different clients without the requirement of data ever leaving the clients. Recent works on FL have advocated taking a Bayesian approach to FL as it offers a principled way to account for the model and predictive uncertainty by learning a posterior distribution for the client and/or server models. Moreover, Bayesian FL also naturally enables personalization in FL to handle data heterogeneity across the different clients by having each client learn its own distinct personalized model. In particular, the hierarchical Bayesian approach enables all the clients to learn their personalized models while also taking into account the commonalities via a prior distribution provided by the server. However, despite their promise, Bayesian approaches for FL can be computationally expensive and can have high communication costs as well because of the requirement of computing and sending the posterior distributions. We present a novel Bayesian FL method using an efficient second-order optimization approach, with a computational cost that is similar to first-order optimization methods like Adam, but also provides the various benefits of the Bayesian approach for FL (e.g., uncertainty, personalization), while also being significantly more efficient and accurate than SOTA Bayesian FL methods (both for standard as well as personalized FL settings). Our method achieves improved predictive accuracies as well as better uncertainty estimates as compared to the baselines which include both optimization based as well as Bayesian FL methods.

Transducer neural networks have emerged as the mainstream approach for streaming automatic speech recognition (ASR), offering state-of-the-art performance in balancing accuracy and latency. In the conventional framework, streaming transducer models are trained to maximize the likelihood function based on non-streaming recursion rules. However, this approach leads to a mismatch between training and inference, resulting in the issue of deformed likelihood and consequently suboptimal ASR accuracy. We introduce a mathematical quantification of the gap between the actual likelihood and the deformed likelihood, namely forward variable causal compensation (FoCC). We also present its estimator, FoCCE, as a solution to estimate the exact likelihood. Through experiments on the LibriSpeech dataset, we show that FoCCE training improves the accuracy of the streaming transducers.

Scientists and engineers use simulators to model empirically observed phenomena. However, tuning the parameters of a simulator to ensure its outputs match observed data presents a significant challenge. Simulation-based inference (SBI) addresses this by enabling Bayesian inference for simulators, identifying parameters that match observed data and align with prior knowledge. Unlike traditional Bayesian inference, SBI only needs access to simulations from the model and does not require evaluations of the likelihood-function. In addition, SBI algorithms do not require gradients through the simulator, allow for massive parallelization of simulations, and can perform inference for different observations without further simulations or training, thereby amortizing inference. Over the past years, we have developed, maintained, and extended $\texttt{sbi}$, a PyTorch-based package that implements Bayesian SBI algorithms based on neural networks. The $\texttt{sbi}$ toolkit implements a wide range of inference methods, neural network architectures, sampling methods, and diagnostic tools. In addition, it provides well-tested default settings but also offers flexibility to fully customize every step of the simulation-based inference workflow. Taken together, the $\texttt{sbi}$ toolkit enables scientists and engineers to apply state-of-the-art SBI methods to black-box simulators, opening up new possibilities for aligning simulations with empirically observed data.