Learn-By-Calibrating: Using Calibration as a Training Objective

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not explicitly measure the uncertainties. This is conceptually similar to heteroscedastic neural networks that produce variance estimates for each prediction, with the key difference that we do not place a Gaussian prior on the predictions. We propose a novel algorithm that performs simultaneous interval estimation for different calibration levels and effectively leverages the intervals to refine the mean estimates. Our results show that, our approach is consistently superior to existing regularization strategies in deep regression models. Finally, we propose to augment partial dependence plots, a model-agnostic interpretability tool, with expected prediction intervals to reveal interesting dependencies between data and the target.

Improving Limited Angle CT Reconstruction with a Robust GAN Prior

Limited angle CT reconstruction is an under-determined linear inverse problem that requires appropriate regularization techniques to be solved. In this work we study how pre-trained generative adversarial networks (GANs) can be used to clean noisy, highly artifact laden reconstructions from conventional techniques, by effectively projecting onto the inferred image manifold. In particular, we use a robust version of the popularly used GAN prior for inverse problems, based on a recent technique called corruption mimicking, that significantly improves the reconstruction quality. The proposed approach operates in the image space directly, as a result of which it does not need to be trained or require access to the measurement model, is scanner agnostic, and can work over a wide range of sensing scenarios.

Exploring Generative Physics Models with Scientific Priors in Inertial Confinement Fusion

There is significant interest in using modern neural networks for scientific applications due to their effectiveness in modeling highly complex, non-linear problems in a data-driven fashion. However, a common challenge is to verify the scientific plausibility or validity of outputs predicted by a neural network. This work advocates the use of known scientific constraints as a lens into evaluating, exploring, and understanding such predictions for the problem of inertial confinement fusion.

Function Preserving Projection for Scalable Exploration of High-Dimensional Data

We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often more interested in determining how one or multiple user-selected response function(s) can be explained by the data. To intuitively connect the responses to the data, FPP constructs 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns of the response functions. More specifically, FPP is designed to (i) produce human-interpretable embeddings; (ii) capture non-linear relationships; (iii) allow the simultaneous use of multiple response functions; and (iv) scale to millions of samples. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in large-scale data that could not be achieved using existing dimension reduction methods.

Building Calibrated Deep Models via Uncertainty Matching with Auxiliary Interval Predictors

With rapid adoption of deep learning in high-regret applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account for the stochasticity of learned models is challenging, it is common to augment predictions with confidence intervals to convey the expected variations in a model's behavior. In general, we require confidence intervals to be well-calibrated, reflect the true uncertainties, and to be sharp. However, most existing techniques for obtaining confidence intervals are known to produce unsatisfactory results in terms of at least one of those criteria. To address this challenge, we develop a novel approach for building calibrated estimators. More specifically, we construct separate models for predicting the target variable, and for estimating the confidence intervals, and pose a bi-level optimization problem that allows the predictive model to leverage estimates from the interval estimator through an \textit{uncertainty matching} strategy. Using experiments in regression, time-series forecasting, and object localization, we show that our approach achieves significant improvements over existing uncertainty quantification methods, both in terms of model fidelity and calibration error.

Distill-to-Label: Weakly Supervised Instance Labeling Using Knowledge Distillation

Weakly supervised instance labeling using only image-level labels, in lieu of expensive fine-grained pixel annotations, is crucial in several applications including medical image analysis. In contrast to conventional instance segmentation scenarios in computer vision, the problems that we consider are characterized by a small number of training images and non-local patterns that lead to the diagnosis. In this paper, we explore the use of multiple instance learning (MIL) to design an instance label generator under this weakly supervised setting. Motivated by the observation that an MIL model can handle bags of varying sizes, we propose to repurpose an MIL model originally trained for bag-level classification to produce reliable predictions for single instances, i.e., bags of size $1$. To this end, we introduce a novel regularization strategy based on virtual adversarial training for improving MIL training, and subsequently develop a knowledge distillation technique for repurposing the trained MIL model. Using empirical studies on colon cancer and breast cancer detection from histopathological images, we show that the proposed approach produces high-quality instance-level prediction and significantly outperforms state-of-the MIL methods.

Scalable Topological Data Analysis and Visualization for Evaluating Data-Driven Models in Scientific Applications

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications.

SALT: Subspace Alignment as an Auxiliary Learning Task for Domain Adaptation

Unsupervised domain adaptation aims to transfer and adapt knowledge learned from a labeled source domain to an unlabeled target domain. Key components of unsupervised domain adaptation include: (a) maximizing performance on the source, and (b) aligning the source and target domains. Traditionally, these tasks have either been considered as separate, or assumed to be implicitly addressed together with high-capacity feature extractors. In this paper, we advance a third broad approach; which we term SALT. The core idea is to consider alignment as an auxiliary task to the primary task of maximizing performance on the source. The auxiliary task is made rather simple by assuming a tractable data geometry in the form of subspaces. We synergistically allow certain parameters derived from the closed-form auxiliary solution, to be affected by gradients from the primary task. The proposed approach represents a unique fusion of geometric and model-based alignment with gradient-flows from a data-driven primary task. SALT is simple, rooted in theory, and outperforms state-of-the-art on multiple standard benchmarks.

A Look at the Effect of Sample Design on Generalization through the Lens of Spectral Analysis

This paper provides a general framework to study the effect of sampling properties of training data on the generalization error of the learned machine learning (ML) models. Specifically, we propose a new spectral analysis of the generalization error, expressed in terms of the power spectra of the sampling pattern and the function involved. The framework is build in the Euclidean space using Fourier analysis and establishes a connection between some high dimensional geometric objects and optimal spectral form of different state-of-the-art sampling patterns. Subsequently, we estimate the expected error bounds and convergence rate of different state-of-the-art sampling patterns, as the number of samples and dimensions increase. We make several observations about generalization error which are valid irrespective of the approximation scheme (or learning architecture) and training (or optimization) algorithms. Our result also sheds light on ways to formulate design principles for constructing optimal sampling methods for particular problems.