Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand complex systems whose internal processes are opaque. Modeling replaces a complex system with a simpler, more interpretable surrogate. Drawing inspiration from this, we construct a class of surrogate models for neural networks using Gaussian processes. Rather than deriving kernels for infinite neural networks, we learn kernels empirically from the naturalistic behavior of finite neural networks. We demonstrate our approach captures existing phenomena related to the spectral bias of neural networks, and then show that our surrogate models can be used to solve practical problems such as identifying which points most influence the behavior of specific neural networks and predicting which architectures and algorithms will generalize well for specific datasets.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of uncertainty are indistinguishable. We present Imprecise Bayesian Neural Networks (IBNNs); they generalize and overcome some of the drawbacks of standard BNNs. These latter are trained using a single prior and likelihood distributions, whereas IBNNs are trained using credal prior and likelihood sets. They allow to distinguish between aleatoric and epistemic uncertainties, and to quantify them. In addition, IBNNs are more robust than BNNs to prior and likelihood misspecification, and to distribution shift. They can also be used to compute sets of outcomes that enjoy probabilistic guarantees. We apply IBNNs to two case studies. One, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. We show that IBNNs performs better when compared to an ensemble of BNNs benchmark.

Many components of data analysis in high energy physics and beyond require morphing one dataset into another. This is commonly solved via reweighting, but there are many advantages of preserving weights and shifting the data points instead. Normalizing flows are machine learning models with impressive precision on a variety of particle physics tasks. Naively, normalizing flows cannot be used for morphing because they require knowledge of the probability density of the starting dataset. In most cases in particle physics, we can generate more examples, but we do not know densities explicitly. We propose a protocol called flows for flows for training normalizing flows to morph one dataset into another even if the underlying probability density of neither dataset is known explicitly. This enables a morphing strategy trained with maximum likelihood estimation, a setup that has been shown to be highly effective in related tasks. We study variations on this protocol to explore how far the data points are moved to statistically match the two datasets. Furthermore, we show how to condition the learned flows on particular features in order to create a morphing function for every value of the conditioning feature. For illustration, we demonstrate flows for flows for toy examples as well as a collider physics example involving dijet events

Existing research has either adapted the Probably Approximately Correct (PAC) Bayesian framework for federated learning (FL) or used information-theoretic PAC-Bayesian bounds while introducing their theorems, but few considering the non-IID challenges in FL. Our work presents the first non-vacuous federated PAC-Bayesian bound tailored for non-IID local data. This bound assumes unique prior knowledge for each client and variable aggregation weights. We also introduce an objective function and an innovative Gibbs-based algorithm for the optimization of the derived bound. The results are validated on real-world datasets.

A set of variables is the Markov blanket of a random variable if it contains all the information needed for predicting the variable. If the blanket cannot be reduced without losing useful information, it is called a Markov boundary. Identifying the Markov boundary of a random variable is advantageous because all variables outside the boundary are superfluous. Hence, the Markov boundary provides an optimal feature set. However, learning the Markov boundary from data is challenging for two reasons. If one or more variables are removed from the Markov boundary, variables outside the boundary may start providing information. Conversely, variables within the boundary may stop providing information. The true role of each candidate variable is only manifesting when the Markov boundary has been identified. In this paper, we propose a new Tsetlin Machine (TM) feedback scheme that supplements Type I and Type II feedback. The scheme introduces a novel Finite State Automaton - a Context-Specific Independence Automaton. The automaton learns which features are outside the Markov boundary of the target, allowing them to be pruned from the TM during learning. We investigate the new scheme empirically, showing how it is capable of exploiting context-specific independence to find Markov boundaries. Further, we provide a theoretical analysis of convergence. Our approach thus connects the field of Bayesian networks (BN) with TMs, potentially opening up for synergies when it comes to inference and learning, including TM-produced Bayesian knowledge bases and TM-based Bayesian inference.

The emergence of a variety of Machine Learning (ML) approaches for travel mode choice prediction poses an interesting question to transport modellers: which models should be used for which applications? The answer to this question goes beyond simple predictive performance, and is instead a balance of many factors, including behavioural interpretability and explainability, computational complexity, and data efficiency. There is a growing body of research which attempts to compare the predictive performance of different ML classifiers with classical random utility models. However, existing studies typically analyse only the disaggregate predictive performance, ignoring other aspects affecting model choice. Furthermore, many studies are affected by technical limitations, such as the use of inappropriate validation schemes, incorrect sampling for hierarchical data, lack of external validation, and the exclusive use of discrete metrics. We address these limitations by conducting a systematic comparison of different modelling approaches, across multiple modelling problems, in terms of the key factors likely to affect model choice (out-of-sample predictive performance, accuracy of predicted market shares, extraction of behavioural indicators, and computational efficiency). We combine several real world datasets with synthetic datasets, where the data generation function is known. The results indicate that the models with the highest disaggregate predictive performance (namely extreme gradient boosting and random forests) provide poorer estimates of behavioural indicators and aggregate mode shares, and are more expensive to estimate, than other models, including deep neural networks and Multinomial Logit (MNL). It is further observed that the MNL model performs robustly in a variety of situations, though ML techniques can improve the estimates of behavioural indices such as Willingness to Pay.

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a novel loss function and a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family. Further, we show that our estimator can be interpreted as a solution to minimizing a particular Bregman score as well as an instance of minimizing the \textit{surrogate} likelihood. We also provide finite sample guarantees to achieve an error (in $\ell_2$-norm) of $\alpha$ in the parameter estimation with sample complexity $O({\sf poly}(k)/\alpha^2)$. Our method achives the order-optimal sample complexity of $O({\sf log}(k)/\alpha^2)$ when tailored for node-wise-sparse Markov random fields. Finally, we demonstrate the performance of our estimator via numerical experiments.

Training energy-based models (EBMs) with maximum likelihood estimation on high-dimensional data can be both challenging and time-consuming. As a result, there a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the initializer model learns to amortize the sampling process of the EBM, and the two models are jointly estimated within a cooperative training framework. Samples from the initializer serve as starting points that are refined by a few sampling steps from the EBM. With the refined samples, the EBM is optimized by maximizing recovery likelihood, while the initializer is optimized by learning from the difference between the refined samples and the initial samples. We develop a new noise schedule and a variance reduction technique to further improve the sample quality. Combining these advances, we significantly boost the FID scores compared to existing EBM methods on CIFAR-10 and ImageNet 32x32, with a 2x speedup over DRL. In addition, we extend our method to compositional generation and image inpainting tasks, and showcase the compatibility of CDRL with classifier-free guidance for conditional generation, achieving similar trade-offs between sample quality and sample diversity as in diffusion models.

A crucial design decision for any robot learning pipeline is the choice of policy representation: what type of model should be used to generate the next set of robot actions? Owing to the inherent multi-modal nature of many robotic tasks, combined with the recent successes in generative modeling, researchers have turned to state-of-the-art probabilistic models such as diffusion models for policy representation. In this work, we revisit the choice of energy-based models (EBM) as a policy class. We show that the prevailing folklore -- that energy models in high dimensional continuous spaces are impractical to train -- is false. We develop a practical training objective and algorithm for energy models which combines several key ingredients: (i) ranking noise contrastive estimation (R-NCE), (ii) learnable negative samplers, and (iii) non-adversarial joint training. We prove that our proposed objective function is asymptotically consistent and quantify its limiting variance. On the other hand, we show that the Implicit Behavior Cloning (IBC) objective is actually biased even at the population level, providing a mathematical explanation for the poor performance of IBC trained energy policies in several independent follow-up works. We further extend our algorithm to learn a continuous stochastic process that bridges noise and data, modeling this process with a family of EBMs indexed by scale variable. In doing so, we demonstrate that the core idea behind recent progress in generative modeling is actually compatible with EBMs. Altogether, our proposed training algorithms enable us to train energy-based models as policies which compete with -- and even outperform -- diffusion models and other state-of-the-art approaches in several challenging multi-modal benchmarks: obstacle avoidance path planning and contact-rich block pushing.