Quantitative descriptions of confidence intervals and uncertainties of the predictions of a model are needed in many applications in vision and machine learning. Mechanisms that enable this for deep neural network (DNN) models are slowly becoming available, and occasionally, being integrated within production systems. But the literature is sparse in terms of how to perform statistical tests with the uncertainties produced by these overparameterized models. For two models with a similar accuracy profile, is the former model's uncertainty behavior better in a statistically significant sense compared to the second model? For high resolution images, performing hypothesis tests to generate meaningful actionable information (say, at a user specified significance level$\alpha=0.05)$is difficult but needed in both mission critical settings and elsewhere. In this paper, specifically for uncertainties defined on images, we show how revisiting results from Random Field theory (RFT) when paired with DNN tools (to get around computational hurdles) leads to efficient frameworks that can provide a hypothesis test capabilities, not otherwise available, for uncertainty maps from models used in many vision tasks. We show via many different experiments the viability of this framework.

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires searching over a class of non-linear functions (e.g., representable by a deep neural network). While effective in practice, the associated runtime/memory costs can increase rapidly, usually as a function of the performance desired in an application. We propose a substantially cheaper (and simpler) forward operator estimation strategy based on adapting known results on kernel transfer operators. We show that our formulation enables highly efficient distribution approximation and sampling, and offers surprisingly good empirical performance that compares favorably with powerful baselines, but with significant runtime savings. We show that the algorithm also performs well in small sample size settings (in brain imaging).

Generative adversarial networks (GANs) have emerged as a powerful generative model in computer vision. Given their impressive abilities in generating highly realistic images, they are also being used in novel ways in applications in the life sciences. This raises an interesting question when GANs are used in scientific or biomedical studies. Consider the setting where we are restricted to only using the samples from a trained GAN for downstream group difference analysis (and do not have direct access to the real data). Will we obtain similar conclusions? In this work, we explore if "generated" data, i.e., sampled from such GANs can be used for performing statistical group difference tests in cases versus controls studies, common across many scientific disciplines. We provide a detailed analysis describing regimes where this may be feasible. We complement the technical results with an empirical study focused on the analysis of cortical thickness on brain mesh surfaces in an Alzheimer's disease dataset. To exploit the geometric nature of the data, we use simple ideas from spectral graph theory to show how adjustments to existing GANs can yield improvements. We also give a generalization error bound by extending recent results on Neural Network Distance. To our knowledge, our work offers the first analysis assessing whether the Null distribution in "healthy versus diseased subjects" type statistical testing using data generated from the GANs coincides with the one obtained from the same analysis with real data. The code is available at https://github.com/yyxiongzju/GLapGAN.

Recent research in deep learning has investigated two very different forms of ''implicitness'': implicit representations model high-frequency data such as images or 3D shapes directly via a low-dimensional neural network (often using e.g., sinusoidal bases or nonlinearities); implicit layers, in contrast, refer to techniques where the forward pass of a network is computed via non-linear dynamical systems, such as fixed-point or differential equation solutions, with the backward pass computed via the implicit function theorem. In this work, we demonstrate that these two seemingly orthogonal concepts are remarkably well-suited for each other. In particular, we show that by exploiting fixed-point implicit layer to model implicit representations, we can substantially improve upon the performance of the conventional explicit-layer-based approach. Additionally, as implicit representation networks are typically trained in large-batch settings, we propose to leverage the property of implicit layers to amortize the cost of fixed-point forward/backward passes over training steps -- thereby addressing one of the primary challenges with implicit layers (that many iterations are required for the black-box fixed-point solvers). We empirically evaluated our method on learning multiple implicit representations for images, videos and audios, showing that our $(\textrm{Implicit})^2$ approach substantially improve upon existing models while being both faster to train and much more memory efficient.

Positron emission tomography (PET) imaging is an imaging modality for diagnosing a number of neurological diseases. In contrast to Magnetic Resonance Imaging (MRI), PET is costly and involves injecting a radioactive substance into the patient. Motivated by developments in modality transfer in vision, we study the generation of certain types of PET images from MRI data. We derive new flow-based generative models which we show perform well in this small sample size regime (much smaller than dataset sizes available in standard vision tasks). Our formulation, DUAL-GLOW, is based on two invertible networks and a relation network that maps the latent spaces to each other. We discuss how given the prior distribution, learning the conditional distribution of PET given the MRI image reduces to obtaining the conditional distribution between the two latent codes w.r.t. the two image types. We also extend our framework to leverage "side" information (or attributes) when available. By controlling the PET generation through "conditioning" on age, our model is also able to capture brain FDG-PET (hypometabolism) changes, as a function of age. We present experiments on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset with 826 subjects, and obtain good performance in PET image synthesis, qualitatively and quantitatively better than recent works.