Related papers: L2M: Practical posterior Laplace approximation wit…
Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…
The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved…
We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model…
First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence,…
Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…
Subspace inference for neural networks assumes that a subspace of their parameter space suffices to produce a reliable uncertainty quantification. In this work, we underpin the validity of this assumption by using low rank techniques. We…
Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…
Stochastic optimization algorithms using exponential moving averages of the past gradients, such as ADAM, RMSProp and AdaGrad, have been having great successes in many applications, especially in training deep neural networks. ADAM in…
We propose a new algorithm for approximating the non-asymptotic second moment of the marginal likelihood estimate, or normalizing constant, provided by a particle filter. The computational cost of the new method is $O(M)$ per time step,…
Adaptive gradient-based optimizers such as Adagrad and Adam are crucial for achieving state-of-the-art performance in machine translation and language modeling. However, these methods maintain second-order statistics for each parameter,…
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…
Optimization algorithms are core methods by which machine learning models iteratively minimize loss functions, update parameters, learn from data, and improve performance. Momentum SGD and AdamW represent two important optimization…