Out-of-distribution (OOD) detection is a critical task in machine learning that seeks to identify abnormal samples. Traditionally, unsupervised methods utilize a deep generative model for OOD detection. However, such approaches require a new model to be trained for each inlier dataset. This paper explores whether a single model can perform OOD detection across diverse tasks. To that end, we introduce Diffusion Paths (DiffPath), which uses a single diffusion model originally trained to perform unconditional generation for OOD detection. We introduce a novel technique of measuring the rate-of-change and curvature of the diffusion paths connecting samples to the standard normal. Extensive experiments show that with a single model, DiffPath is competitive with prior work using individual models on a variety of OOD tasks involving different distributions. Our code is publicly available at https://github.com/clear-nus/diffpath.

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.

Locating semantically meaningful landmark points is a crucial component of a large number of computer vision pipelines. Because of the small number of available datasets with ground truth landmark annotations, it is essential to design robust unsupervised and semi-supervised methods for landmark detection. Many of the recent unsupervised learning methods rely on the equivariance properties of landmarks to synthetic image deformations. Our work focuses on such widely used methods and sheds light on its core problem, its inability to produce equivariant intermediate convolutional features. This finding leads us to formulate a two-step unsupervised approach that overcomes this challenge by first learning powerful pixel-based features that are then exploited in a second step within standard landmark detection approaches. Our methodology produces state-of-the-art results on several benchmarks such as the BBC Pose dataset, the Cat-head dataset and performs comparably in other situations.

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. This text examines the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. We demonstrate that, although standard ensembling techniques certainly help to boost accuracy, the calibration of deep ensembles relies on subtle trade-offs. We also find that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that, in the low data regime, this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems when compared to standard deep-ensembles.

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the whole data set. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem by generating proposals which are only based on a subset of the data, by skipping the accept-reject step and by using decreasing step-sizes sequence $(\delta_m)_{m \geq 0}$. We provide in this article a rigorous mathematical framework for analysing this algorithm. We prove that, under verifiable assumptions, the algorithm is consistent, satisfies a central limit theorem (CLT) and its asymptotic bias-variance decomposition can be characterized by an explicit functional of the step-sizes sequence $(\delta_m)_{m \geq 0}$. We leverage this analysis to give practical recommendations for the notoriously difficult tuning of this algorithm: it is asymptotically optimal to use a step-size sequence of the type $\delta_m \asymp m^{-1/3}$, leading to an algorithm whose mean squared error (MSE) decreases at rate $\mathcal{O}(m^{-1/3})$.