Gaussian processes are now commonly used in dimensionality reduction approaches tailored to neuroscience, especially to describe changes in high-dimensional neural activity over time. As recording capabilities expand to include neuronal populations across multiple brain areas, cortical layers, and cell types, interest in extending Gaussian process factor models to characterize multi-population interactions has grown. However, the cubic runtime scaling of current methods with the length of experimental trials and the number of recorded populations (groups) precludes their application to large-scale multi-population recordings. Here, we improve this scaling from cubic to linear in both trial length and group number. We present two approximate approaches to fitting multi-group Gaussian process factor models based on (1) inducing variables and (2) the frequency domain. Empirically, both methods achieved orders of magnitude speed-up with minimal impact on statistical performance, in simulation and on neural recordings of hundreds of neurons across three brain areas. The frequency domain approach, in particular, consistently provided the greatest runtime benefits with the fewest trade-offs in statistical performance. We further characterize the estimation biases introduced by the frequency domain approach and demonstrate effective strategies to mitigate them. This work enables a powerful class of analysis techniques to keep pace with the growing scale of multi-population recordings, opening new avenues for exploring brain function.

Learning-based solutions for long-tailed recognition face difficulties in generalizing on balanced test datasets. Due to imbalanced data prior, the learned \textit{a posteriori} distribution is biased toward the most frequent (head) classes, leading to an inferior performance on the least frequent (tail) classes. In general, the performance can be improved by removing such a bias by eliminating the effect of imbalanced prior modeled using the number of class samples (frequencies). We first observe that the \textit{effective prior} on the classes, learned by the model at the end of the training, can differ from the empirical prior obtained using class frequencies. Thus, we propose a novel approach to accurately model the effective prior of a trained model using \textit{a posteriori} probabilities. We propose to correct the imbalanced prior by adjusting the predicted \textit{a posteriori} probabilities (Prior2Posterior: P2P) using the calculated prior in a post-hoc manner after the training, and show that it can result in improved model performance. We present theoretical analysis showing the optimality of our approach for models trained with naive cross-entropy loss as well as logit adjusted loss. Our experiments show that the proposed approach achieves new state-of-the-art (SOTA) on several benchmark datasets from the long-tail literature in the category of logit adjustment methods. Further, the proposed approach can be used to inspect any existing method to capture the \textit{effective prior} and remove any residual bias to improve its performance, post-hoc, without model retraining. We also show that by using the proposed post-hoc approach, the performance of many existing methods can be improved further.

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often necessary for downstream tasks. Finding an accurate approximation to this posterior is challenging, due to the large number of possible causal graphs, as well as the difficulty in the subproblem of finding posteriors over the functional relationships of the causal edges. Recent works have used meta-learning to view the problem of estimating the maximum a-posteriori causal graph as supervised learning. Yet, these methods are limited when estimating the full posterior as they fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. Further, these methods also cannot reliably sample from the posterior over causal structures. To address these limitations, we propose a Bayesian meta learning model that allows for sampling causal structures from the posterior and encodes these key properties. We compare our meta-Bayesian causal discovery against existing Bayesian causal discovery methods, demonstrating the advantages of directly learning a posterior over causal structure.

Recently, discrete diffusion language models have demonstrated promising results in NLP. However, there has been limited research on integrating Pretrained Language Models (PLMs) into discrete diffusion models, resulting in underwhelming performance in downstream NLP generation tasks. This integration is particularly challenging because of the discrepancy between step-wise denoising strategy of diffusion models and single-step mask prediction approach of MLM-based PLMs. In this paper, we introduce Diffusion-EAGS, a novel approach that effectively integrates PLMs with the diffusion models. Furthermore, as it is challenging for PLMs to determine where to apply denoising during the diffusion process, we integrate an entropy tracking module to assist them. Finally, we propose entropy-based noise scheduling in the forward process to improve the effectiveness of entropy-adaptive sampling throughout the generation phase. Experimental results show that Diffusion-EAGS outperforms existing diffusion baselines in downstream generation tasks, achieving high text quality and diversity with precise token-level control. We also show that our model is capable of adapting to bilingual and low-resource settings, which are common in real-world applications.

The debate between scientific realism and anti-realism remains at a stalemate, making reconciliation seem hopeless. Yet, important work remains: exploring a common ground, even if only to uncover deeper points of disagreement and, ideally, to benefit both sides of the debate. I propose such a common ground. Specifically, many anti-realists, such as instrumentalists, have yet to seriously engage with Sober's call to justify their preferred version of Ockham's razor through a positive account. Meanwhile, realists face a similar challenge: providing a non-circular explanation of how their version of Ockham's razor connects to truth. The common ground I propose addresses these challenges for both sides; the key is to leverage the idea that everyone values some truths and to draw on insights from scientific fields that study scientific inference -- namely, statistics and machine learning. This common ground also isolates a distinctively epistemic root of the irreconcilability in the realism debate.

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range of applications, in particular when the relevant variables are known and at the same level of abstraction. However, the given variables can also be unstructured data, like pixels of an image. Meanwhile, the causal variables, such as the positions of objects in the image, can be arbitrary deterministic functions of the given variables. Moreover, the causal variables may form a hierarchy of abstractions, in which the macro-level variables are deterministic functions of the micro-level variables. Causal graphs are limited when it comes to modeling this kind of situation. In the presence of deterministic relationships there is generally no causal graph that satisfies both the Markov condition and the faithfulness condition. We introduce factored space models as an alternative to causal graphs which naturally represent both probabilistic and deterministic relationships at all levels of abstraction. Moreover, we introduce structural independence and establish that it is equivalent to statistical independence in every distribution that factorizes over the factored space. This theorem generalizes the classical soundness and completeness theorem for d-separation.

Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points of the data density. For valley point detection, we introduce properties of critical points on the convex hull of the empirical cumulative density function (ecdf) plot that provide indications on the existence of density valleys. Next, we apply a unimodal data modeling approach that provides a statistical model for each obtained unimodal subset in the form of a Uniform Mixture Model (UMM). Consequently, a hierarchical statistical model of the initial dataset is obtained in the form of a mixture of UMMs, named as the Unimodal Mixture Model (UDMM). The proposed method is non-parametric, hyperparameter-free, automatically estimates the number of unimodal subsets and provides accurate statistical models as indicated by experimental results on clustering and density estimation tasks.

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we discuss function space inference via particle optimization and present practical modifications that improve uncertainty estimation and, most importantly, make it applicable for large and pretrained networks. First, we demonstrate that the input samples, where particle predictions are enforced to be diverse, are detrimental to the model performance. While diversity on training data itself can lead to underfitting, the use of label-destroying data augmentation, or unlabeled out-of-distribution data can improve prediction diversity and uncertainty estimates. Furthermore, we take advantage of the function space formulation, which imposes no restrictions on network parameterization other than sufficient flexibility. Instead of using full deep ensembles to represent particles, we propose a single multi-headed network that introduces a minimal increase in parameters and computation. This allows seamless integration to pretrained networks, where this repulsive last-layer ensemble can be used for uncertainty aware fine-tuning at minimal additional cost. We achieve competitive results in disentangling aleatoric and epistemic uncertainty for active learning, detecting out-of-domain data, and providing calibrated uncertainty estimates under distribution shifts with minimal compute and memory.

We study the dynamics of gradient flow in high dimensions for the multi-spiked tensor problem, where the goal is to estimate $r$ unknown signal vectors (spikes) from noisy Gaussian tensor observations. Specifically, we analyze the maximum likelihood estimation procedure, which involves optimizing a highly nonconvex random function. We determine the sample complexity required for gradient flow to efficiently recover all spikes, without imposing any assumptions on the separation of the signal-to-noise ratios (SNRs). More precisely, our results provide the sample complexity required to guarantee recovery of the spikes up to a permutation. Our work builds on our companion paper [Ben Arous, Gerbelot, Piccolo 2024], which studies Langevin dynamics and determines the sample complexity and separation conditions for the SNRs necessary for ensuring exact recovery of the spikes (where the recovered permutation matches the identity). During the recovery process, the correlations between the estimators and the hidden vectors increase in a sequential manner. The order in which these correlations become significant depends on their initial values and the corresponding SNRs, which ultimately determines the permutation of the recovered spikes.

Precise identification of dynamic models in robotics is essential to support control design, friction compensation, output torque estimation, etc. A longstanding challenge remains in the identification of friction models for robotic joints, given the numerous physical phenomena affecting the underlying friction dynamics which result into nonlinear characteristics and hysteresis behaviour in particular. These phenomena proof difficult to be modelled and captured accurately using physical analogies alone. This has motivated researchers to shift from physics-based to data-driven models. Currently, these methods are still limited in their ability to generalize effectively to typical industrial robot deployement, characterized by high- and low-velocity operations and frequent direction reversals. Empirical observations motivate the use of dynamic friction models but these remain particulary challenging to establish. To address the current limitations, we propose to account for unidentified dynamics in the robot joints using latent dynamic states. The friction model may then utilize both the dynamic robot state and additional information encoded in the latent state to evaluate the friction torque. We cast this stochastic and partially unsupervised identification problem as a standard probabilistic representation learning problem. In this work both the friction model and latent state dynamics are parametrized as neural networks and integrated in the conventional lumped parameter dynamic robot model. The complete dynamics model is directly learned from the noisy encoder measurements in the robot joints. We use the Expectation-Maximisation (EM) algorithm to find a Maximum Likelihood Estimate (MLE) of the model parameters. The effectiveness of the proposed method is validated in terms of open-loop prediction accuracy in comparison with baseline methods, using the Kuka KR6 R700 as a test platform.