Related papers: laplax -- Laplace Approximations with JAX

CLAX is a JAX-based library that implements classic click models using modern gradient-based optimization. While neural click models have emerged over the past decade, complex click models based on probabilistic graphical models (PGMs) have…

Identifying the obstacle space is crucial for path planning. However, generating an accurate obstacle space remains a significant challenge due to various sources of uncertainty, including motion, behavior, and perception limitations. Even…

Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In…

We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an…

This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by…

In Bayesian Deep Learning, distributions over the output of classification neural networks are often approximated by first constructing a Gaussian distribution over the weights, then sampling from it to receive a distribution over the…

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on…

The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that…

This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our…

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA…

Neural networks' expressiveness comes at the cost of complex, black-box models that often extrapolate poorly beyond the domain of the training dataset, conflicting with the goal of finding compact analytic expressions to describe scientific…

Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension…

The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…

This paper introduces Laplace techniques for designing a neural network, with the goal of estimating simplex-constraint sparse vectors from compressed measurements. To this end, we recast the problem of MMSE estimation (w.r.t. a pre-defined…

We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate…

For a broad variety of critical applications, it is essential to know how confident a classification prediction is. In this paper, we discuss the drawbacks of softmax to calculate class probabilities and to handle uncertainty in Bayesian…

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms.…