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We establish explicit dynamics for neural networks whose training objective has a regularising term that constrains the parameters to remain close to their initial value. This keeps the network in a lazy training regime, where the dynamics can be linearised around the initialisation. The standard neural tangent kernel (NTK) governs the evolution during the training in the infinite-width limit, although the regularisation yields an additional term appears in the differential equation describing the dynamics. This setting provides an appropriate framework to study the evolution of wide networks trained to optimise generalisation objectives such as PAC-Bayes bounds, and hence potentially contribute to a deeper theoretical understanding of such networks.

Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite their widespread use in both statistical and non-statistical applications, very little is known about their convergence properties. This article introduces novel methods for establishing bounds on the convergence rates of hybrid Gibbs samplers. In particular, we examine the convergence characteristics of hybrid random-scan Gibbs and data augmentation algorithms. Our analysis reveals that the absolute spectral gap of a reversible hybrid chain can be bounded based on the absolute spectral gap of the exact Gibbs chain and the absolute spectral gaps of the Markov chains employed for conditional distribution approximations. The new techniques are applied to four algorithms: a random-scan Metropolis-within-Gibbs sampler, a hybrid proximal sampler, random-scan Gibbs samplers with block updates, and a hybrid slice sampler.

Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent variables and data interact through more complex designs. In this work, we study empirical Bayes estimation of an i.i.d. prior in Bayesian linear models, via the nonparametric maximum likelihood estimator (NPMLE). We introduce and study a system of gradient flow equations for optimizing the marginal log-likelihood, jointly over the prior and posterior measures in its Gibbs variational representation using a smoothed reparametrization of the regression coefficients. A diffusion-based implementation yields a Langevin dynamics MCEM algorithm, where the prior law evolves continuously over time to optimize a sequence-model log-likelihood defined by the coordinates of the current Langevin iterate. We show consistency of the NPMLE as $n, p \rightarrow \infty$ under mild conditions, including settings of random sub-Gaussian designs when $n \asymp p$. In high noise, we prove a uniform log-Sobolev inequality for the mixing of Langevin dynamics, for possibly misspecified priors and non-log-concave posteriors. We then establish polynomial-time convergence of the joint gradient flow to a near-NPMLE if the marginal negative log-likelihood is convex in a sub-level set of the initialization.

We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.

In areal unit data with missing or suppressed data, it desirable to create models that are able to predict observations that are not available. Traditional statistical methods achieve this through Bayesian hierarchical models that can capture the unexplained residual spatial autocorrelation through conditional autoregressive (CAR) priors, such that they can make predictions at geographically related spatial locations. In contrast, typical machine learning approaches such as random forests ignore this residual autocorrelation, and instead base predictions on complex non-linear feature-target relationships. In this paper, we propose CAR-Forest, a novel spatial prediction algorithm that combines the best features of both approaches by fusing them together. By iteratively refitting a random forest combined with a Bayesian CAR model in one algorithm, CAR-Forest can incorporate flexible feature-target relationships while still accounting for the residual spatial autocorrelation. Our results, based on a Scottish housing price data set, show that CAR-Forest outperforms Bayesian CAR models, random forests, and the state-of-the-art hybrid approach, geographically weighted random forest, providing a state-of-the-art framework for small-area spatial prediction.

Detection and identification of emitters provide vital information for defensive strategies in electronic intelligence. Based on a received signal containing pulses from an unknown number of emitters, this paper introduces an unsupervised methodology for deinterleaving RADAR signals based on a combination of clustering algorithms and optimal transport distances. The first step involves separating the pulses with a clustering algorithm under the constraint that the pulses of two different emitters cannot belong to the same cluster. Then, as the emitters exhibit complex behavior and can be represented by several clusters, we propose a hierarchical clustering algorithm based on an optimal transport distance to merge these clusters. A variant is also developed, capable of handling more complex signals. Finally, the proposed methodology is evaluated on simulated data provided through a realistic simulator. Results show that the proposed methods are capable of deinterleaving complex RADAR signals.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

This work compares three locomotion techniques for an immersive VR environment: two different types of teleporting (with and without animation) and a manual (joystick-based) technique. We tested the effect of these techniques on visual motion sickness, spatial awareness, presence, subjective pleasantness, and perceived difficulty of operating the navigation. We collected eye tracking and head and body orientation data to investigate the relationships between motion, vection, and sickness. Our study confirms some results already discussed in the literature regarding the reduced invasiveness and the high usability of instant teleport while increasing the evidence against the hypothesis of reduced spatial awareness induced by this technique. We reinforce the evidence about the issues of extending teleporting with animation. Furthermore, we offer some new evidence of a benefit to the user experience of the manual technique and the correlation of the sickness felt in this condition with head movements. The findings of this study contribute to the ongoing debate on the development of guidelines on navigation interfaces in specific VR environments.

Training large transformer models from scratch for a target task requires lots of data and is computationally demanding. The usual practice of transfer learning overcomes this challenge by initializing the model with weights of a pretrained model of the same size and specification to increase the convergence and training speed. However, what if no pretrained model of the required size is available? In this paper, we introduce a simple yet effective technique to transfer the knowledge of a pretrained model to smaller variants. Our approach called weight subcloning expedites the training of scaled-down transformers by initializing their weights from larger pretrained models. Weight subcloning involves an operation on the pretrained model to obtain the equivalent initialized scaled-down model. It consists of two key steps: first, we introduce neuron importance ranking to decrease the embedding dimension per layer in the pretrained model. Then, we remove blocks from the transformer model to match the number of layers in the scaled-down network. The result is a network ready to undergo training, which gains significant improvements in training speed compared to random initialization. For instance, we achieve 4x faster training for vision transformers in image classification and language models designed for next token prediction.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.