Miracle-dz/UniFAR-FTUs huggingface dataset:
Normalizing Flow Ensembles for Rich Aleatoric and Epistemic Uncertainty Modeling

In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are state-of-the-art in modeling aleatoric uncertainty. The ensembles are created via sets of fixed dropout masks, making them less expensive than creating separate NF models. We demonstrate how to leverage the unique structure of NFs, base distributions, to estimate aleatoric uncertainty without relying on samples, provide a comprehensive set of baselines, and derive unbiased estimates for differential entropy. The methods were applied to a variety of experiments, commonly used to benchmark aleatoric and epistemic uncertainty estimation: 1D sinusoidal data, 2D windy grid-world (Wet Chicken), Pendulum, and Hopper. In these experiments, we setup an active learning framework and evaluate each model's capability at measuring aleatoric and epistemic uncertainty. The results show the advantages of using NF ensembles in capturing complicated aleatoric while maintaining accurate epistemic uncertainty estimates.
Dual Propagation: Accelerating Contrastive Hebbian Learning with Dyadic Neurons

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.
Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs

Dynamic graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real-world applications such as intrusion identification in network systems, detection of ecosystem disturbances, and detection of epidemic outbreaks. In this article, we focus on change point detection in dynamic graphs and address three main challenges associated with this problem: (i) how to compare graph snapshots across time, (ii) how to capture temporal dependencies, and (iii) how to combine different views of a temporal graph. To solve the above challenges, we first propose Laplacian Anomaly Detection (LAD) which uses the spectrum of graph Laplacian as the low dimensional embedding of the graph structure at each snapshot. LAD explicitly models short-term and long-term dependencies by applying two sliding windows. Next, we propose MultiLAD, a simple and effective generalization of LAD to multi-view graphs. MultiLAD provides the first change point detection method for multi-view dynamic graphs. It aggregates the singular values of the normalized graph Laplacian from different views through the scalar power mean operation. Through extensive synthetic experiments, we show that (i) LAD and MultiLAD are accurate and outperforms state-of-the-art baselines and their multi-view extensions by a large margin, (ii) MultiLAD’s advantage over contenders significantly increases when additional views are available, and (iii) MultiLAD is highly robust to noise from individual views. In five real-world dynamic graphs, we demonstrate that LAD and MultiLAD identify significant events as top anomalies such as the implementation of government COVID-19 interventions which impacted the population mobility in multi-view traffic networks.
Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, and the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability by using a representation theorem for analytic functions of exponential type.
Diversity Through Exclusion (DTE): Niche Identification for Reinforcement Learning through Value-Decomposition

Many environments contain numerous available niches of variable value, each associated with a different local optimum in the space of behaviors (policy space). In such situations it is often difficult to design a learning process capable of evading distraction by poor local optima long enough to stumble upon the best available niche. In this work we propose a generic reinforcement learning (RL) algorithm that performs better than baseline deep Q-learning algorithms in such environments with multiple variably-valued niches. The algorithm we propose consists of two parts: an agent architecture and a learning rule. The agent architecture contains multiple sub-policies. The learning rule is inspired by fitness sharing in evolutionary computation and applied in reinforcement learning using Value-Decomposition-Networks in a novel manner for a single-agent's internal population. It can concretely be understood as adding an extra loss term where one policy's experience is also used to update all the other policies in a manner that decreases their value estimates for the visited states. In particular, when one sub-policy visits a particular state frequently this decreases the value predicted for other sub-policies for going to that state. Further, we introduce an artificial chemistry inspired platform where it is easy to create tasks with multiple rewarding strategies utilizing different resources (i.e. multiple niches). We show that agents trained this way can escape poor-but-attractive local optima to instead converge to harder-to-discover higher value strategies in both the artificial chemistry environments and in simpler illustrative environments.
Fast Online Value-Maximizing Prediction Sets with Conformal Cost Control

Many real-world multi-label prediction problems involve set-valued predictions that must satisfy specific requirements dictated by downstream usage. We focus on a typical scenario where such requirements, separately encoding $\textit{value}$ and $\textit{cost}$, compete with each other. For instance, a hospital might expect a smart diagnosis system to capture as many severe, often co-morbid, diseases as possible (the value), while maintaining strict control over incorrect predictions (the cost). We present a general pipeline, dubbed as FavMac, to maximize the value while controlling the cost in such scenarios. FavMac can be combined with almost any multi-label classifier, affording distribution-free theoretical guarantees on cost control. Moreover, unlike prior works, it can handle real-world large-scale applications via a carefully designed online update mechanism, which is of independent interest. Our methodological and theoretical contributions are supported by experiments on several healthcare tasks and synthetic datasets - FavMac furnishes higher value compared with several variants and baselines while maintaining strict cost control. Our code is available at https://github.com/zlin7/FavMac
Average-Constrained Policy Optimization

Reinforcement Learning (RL) with constraints is becoming an increasingly important problem for various applications. Often, the average criterion is more suitable than the discounted criterion. Yet, RL for average criterion-constrained MDPs remains a challenging problem. Algorithms designed for discounted constrained RL problems often do not perform well for the average CMDP setting. In this paper, we introduce a new policy optimization with function approximation algorithm for constrained MDPs with the average criterion. The Average-Constrained Policy Optimization (ACPO) algorithm is inspired by the famed PPO-type algorithms based on trust region methods. We develop basic sensitivity theory for average MDPs, and then use the corresponding bounds in the design of the algorithm. We provide theoretical guarantees on its performance, and through extensive experimental work in various challenging MuJoCo environments, show the superior performance of the algorithm when compared to other state-of-the-art algorithms adapted for the average CMDP setting.
Sample Complexity of Kernel-Based Q-Learning

Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive statistically efficient RL policies handling large state-action spaces, with more general Q-functions, some recent works have considered nonlinear function approximation using kernel ridge regression. In this work, we derive sample complexities for kernel based Q-learning when a generative model exists. We propose a nonparametric Q-learning algorithm which finds an $\epsilon$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $\epsilon$ and the complexity of the kernel (in terms of its information gain). To the best of our knowledge, this is the first result showing a finite sample complexity under such a general model.
A Bayesian analysis of current duration data with reporting issues: an application to estimating the distribution of time-between-sex from time since-last-sex data as collected in cross-sectional surveys in low- and middle-income countries

Aggregate measures of family planning are used to monitor demand for and usage of contraceptive methods in populations globally, for example as part of the FP2030 initiative. Family planning measures for low- and middle-income countries are typically based on data collected through cross-sectional household surveys. Recently proposed measures account for sexual activity through assessment of the distribution of time-between-sex (TBS) in the population of interest. In this paper, we propose a statistical approach to estimate the distribution of TBS using data typically available in low- and middle-income countries, while addressing two major challenges. The first challenge is that timing of sex information is typically limited to women's time-since-last-sex (TSLS) data collected in the cross-sectional survey. In our proposed approach, we adopt the current duration method to estimate the distribution of TBS using the available TSLS data, from which the frequency of sex at the population level can be derived. Furthermore, the observed TSLS data are subject to reporting issues because they can be reported in different units and may be rounded off. To apply the current duration approach and account for these data reporting issues, we develop a flexible Bayesian model, and provide a detailed technical description of the proposed modeling approach.
TransFool: An Adversarial Attack against Neural Machine Translation Models

Deep neural networks have been shown to be vulnerable to small perturbations of their inputs, known as adversarial attacks. In this paper, we investigate the vulnerability of Neural Machine Translation (NMT) models to adversarial attacks and propose a new attack algorithm called TransFool. To fool NMT models, TransFool builds on a multi-term optimization problem and a gradient projection step. By integrating the embedding representation of a language model, we generate fluent adversarial examples in the source language that maintain a high level of semantic similarity with the clean samples. Experimental results demonstrate that, for different translation tasks and NMT architectures, our white-box attack can severely degrade the translation quality while the semantic similarity between the original and the adversarial sentences stays high. Moreover, we show that TransFool is transferable to unknown target models. Finally, based on automatic and human evaluations, TransFool leads to improvement in terms of success rate, semantic similarity, and fluency compared to the existing attacks both in white-box and black-box settings. Thus, TransFool permits us to better characterize the vulnerability of NMT models and outlines the necessity to design strong defense mechanisms and more robust NMT systems for real-life applications.
Physics Informed Piecewise Linear Neural Networks for Process Optimization

Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from issues such as overfitting and lack of useful and highquality data. At the same time, embedding trained machine learning models directly into the optimization problems has become an effective and state-of-the-art approach for surrogate optimization, whose performance can be improved by physics-informed training. In this study, it is proposed to upgrade piece-wise linear neural network models with physics informed knowledge for optimization problems with neural network models embedded. In addition to using widely accepted and naturally piece-wise linear rectified linear unit (ReLU) activation functions, this study also suggests piece-wise linear approximations for the hyperbolic tangent activation function to widen the domain. Optimization of three case studies, a blending process, an industrial distillation column and a crude oil column are investigated. For all cases, physics-informed trained neural network based optimal results are closer to global optimality. Finally, associated CPU times for the optimization problems are much shorter than the standard optimization results.
ImageNomer: developing an fMRI and omics visualization tool to detect racial bias in functional connectivity

It can be difficult to identify trends and perform quality control in large, high-dimensional fMRI or omics datasets. To remedy this, we develop ImageNomer, a data visualization and analysis tool that allows inspection of both subject-level and cohort-level features. The tool allows visualization of phenotype correlation with functional connectivity (FC), partial connectivity (PC), dictionary components (PCA and our own method), and genomic data (single-nucleotide polymorphisms, SNPs). In addition, it allows visualization of weights from arbitrary ML models. ImageNomer is built with a Python backend and a Vue frontend. We validate ImageNomer using the Philadelphia Neurodevelopmental Cohort (PNC) dataset, which contains multitask fMRI and SNP data of healthy adolescents. Using correlation, greedy selection, or model weights, we find that a set of 10 FC features can explain 15% of variation in age, compared to 35% for the full 34,716 feature model. The four most significant FCs are either between bilateral default mode network (DMN) regions or spatially proximal subcortical areas. Additionally, we show that whereas both FC (fMRI) and SNPs (genomic) features can account for 10-15% of intelligence variation, this predictive ability disappears when controlling for race. We find that FC features can be used to predict race with 85% accuracy, compared to 78% accuracy for sex prediction. Using ImageNomer, this work casts doubt on the possibility of finding unbiased intelligence-related features in fMRI and SNPs of healthy adolescents.
Multimodal Chain-of-Thought Reasoning in Language Models

Large language models (LLMs) have shown impressive performance on complex reasoning by leveraging chain-of-thought (CoT) prompting to generate intermediate reasoning chains as the rationale to infer the answer. However, existing CoT studies have focused on the language modality. We propose Multimodal-CoT that incorporates language (text) and vision (images) modalities into a two-stage framework that separates rationale generation and answer inference. In this way, answer inference can leverage better generated rationales that are based on multimodal information. With Multimodal-CoT, our model under 1 billion parameters outperforms the previous state-of-the-art LLM (GPT-3.5) by 16 percentage points (75.17%->91.68% accuracy) on the ScienceQA benchmark and even surpasses human performance. Code is publicly available available at https://github.com/amazon-science/mm-cot.
Comparing regression curves -- an $L^1$-point of view

In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study.
The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing

We propose $\textsf{ScaledGD($\lambda$)}$, a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, $\textsf{ScaledGD($\lambda$)}$ starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, $\textsf{ScaledGD($\lambda$)}$ is remarkably robust to ill-conditioning compared to vanilla gradient descent ($\textsf{GD}$) even with overprameterization. Specifically, we show that, under the Gaussian design, $\textsf{ScaledGD($\lambda$)}$ converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla $\textsf{GD}$ which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.
A ONE DIMENSIONAL QUANTUM TRANSPORT MODEL WITH SMALL COHERENCE LENGTHS

ABSTRACT A one dimensional stationary transport model accounting for both quantum effects and smallness of coherence length is presented and analyzed. The physical system extension is an interval [a,b] whose length is of the order of few to several times the coherence length of particles. An arbitrary decomposition of the interval into intervals of lengths comparable to coherence length is chosen. On each interval, the particle density is the superposition of densities of scattering states of the Schrodinger equation. The statistics in the various intervals are solution of a linear system whose coefficients depend on the reflexion and transmission coefficients. This system is shown to have a unique minimal solution. In the limit of very small coherence lengths, a collisionless kinetic equation is obtained.
Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models

Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.
Sample-efficient Surrogate Model for Frequency Response of Linear PDEs using Self-Attentive Complex Polynomials

Linear Partial Differential Equations (PDEs) govern the spatial-temporal dynamics of physical systems that are essential to building modern technology. When working with linear PDEs, designing a physical system for a specific outcome is difficult and costly due to slow and expensive explicit simulation of PDEs and the highly nonlinear relationship between a system's configuration and its behavior. In this work, we prove a parametric form that certain physical quantities in the Fourier domain must obey in linear PDEs, named the CZP (Constant-Zeros-Poles) framework. Applying CZP to antenna design, an industrial application using linear PDEs (i.e., Maxwell's equations), we derive a sample-efficient parametric surrogate model that directly predicts its scattering coefficients without explicit numerical PDE simulation. Combined with a novel image-based antenna representation and an attention-based neural network architecture, CZP outperforms baselines by 10% to 25% in terms of test loss and also is able to find 2D antenna designs verifiable by commercial software with $33\%$ greater success than baselines, when coupled with sequential search techniques like reinforcement learning.
Boundary-Aware Uncertainty for Feature Attribution Explainers

Post-hoc explanation methods have become a critical tool for understanding black-box classifiers in high-stakes applications. However, high-performing classifiers are often highly nonlinear and can exhibit complex behavior around the decision boundary, leading to brittle or misleading local explanations. Therefore there is an impending need to quantify the uncertainty of such explanation methods in order to understand when explanations are trustworthy. In this work we propose the Gaussian Process Explanation UnCertainty (GPEC) framework, which generates a unified uncertainty estimate combining decision boundary-aware uncertainty with explanation function approximation uncertainty. We introduce a novel geodesic-based kernel, which captures the complexity of the target black-box decision boundary. We show theoretically that the proposed kernel similarity increases with decision boundary complexity. The proposed framework is highly flexible; it can be used with any black-box classifier and feature attribution method. Empirical results on multiple tabular and image datasets show that the GPEC uncertainty estimate improves understanding of explanations as compared to existing methods.