This article investigates uncertainty quantification of the generalized linear lasso~(GLL), a popular variable selection method in high-dimensional regression settings. In many fields of study, researchers use data-driven methods to select a subset of variables that are most likely to be associated with a response variable. However, such variable selection methods can introduce bias and increase the likelihood of false positives, leading to incorrect conclusions. In this paper, we propose a post-selection inference framework that addresses these issues and allows for valid statistical inference after variable selection using GLL. We show that our method provides accurate $p$-values and confidence intervals, while maintaining high statistical power. In a second stage, we focus on the sparse logistic regression, a popular classifier in high-dimensional statistics. We show with extensive numerical simulations that SIGLE is more powerful than state-of-the-art PSI methods. SIGLE relies on a new method to sample states from the distribution of observations conditional on the selection event. This method is based on a simulated annealing strategy whose energy is given by the first order conditions of the logistic lasso.
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Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and goals. To address these challenges, we show a connection between differential games, optimal control, and energy-based models and demonstrate how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this formulation, this work introduces a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The experiments using simulated mobile robot pedestrian interactions and real-world automated driving data provide empirical evidence that the game-theoretic layer improves the predictive performance of various neural network backbones.
Implicit neural networks have demonstrated remarkable success in various tasks. However, there is a lack of theoretical analysis of the connections and differences between implicit and explicit networks. In this paper, we study high-dimensional implicit neural networks and provide the high dimensional equivalents for the corresponding conjugate kernels and neural tangent kernels. Built upon this, we establish the equivalence between implicit and explicit networks in high dimensions.
This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting its dynamics and, as a consequence, Noether's Theorem, conserved quantities are observed. We propose to simulate and learn the mappings of interest through the construction of $G$-invariant Lagrangian submanifolds, which are pivotal objects in symplectic geometry. A notable property of our constructions is that the simulated/learned dynamics also preserves the same conserved quantities as the original system, resulting in a more faithful surrogate of the original dynamics than non-symmetry aware methods, and in a more accurate predictor of non-observed trajectories. Furthermore, our setting is able to simulate/learn not only Hamiltonian flows, but any Lie group-equivariant symplectic transformation. Our designs leverage pivotal techniques and concepts in symplectic geometry and geometric mechanics: reduction theory, Noether's Theorem, Lagrangian submanifolds, momentum mappings, and coisotropic reduction among others. We also present methods to learn Poisson transformations while preserving the underlying geometry and how to endow non-geometric integrators with geometric properties. Thus, this work presents a novel attempt to harness the power of symplectic and Poisson geometry towards simulating and learning problems.
In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring $k$-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both $k$-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel $k$-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in $k$-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional $k$-space interpolation methods, deep learning-based $k$-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.
Generative Adversarial Networks (GANs) have shown success in approximating complex distributions for synthetic image generation. However, current GAN-based methods for generating biometric images, such as iris, have certain limitations: (a) the synthetic images often closely resemble images in the training dataset; (b) the generated images lack diversity in terms of the number of unique identities represented in them; and (c) it is difficult to generate multiple images pertaining to the same identity. To overcome these issues, we propose iWarpGAN that disentangles identity and style in the context of the iris modality by using two transformation pathways: Identity Transformation Pathway to generate unique identities from the training set, and Style Transformation Pathway to extract the style code from a reference image and output an iris image using this style. By concatenating the transformed identity code and reference style code, iWarpGAN generates iris images with both inter- and intra-class variations. The efficacy of the proposed method in generating such iris DeepFakes is evaluated both qualitatively and quantitatively using ISO/IEC 29794-6 Standard Quality Metrics and the VeriEye iris matcher. Further, the utility of the synthetically generated images is demonstrated by improving the performance of deep learning based iris matchers that augment synthetic data with real data during the training process.
People are increasingly turning to large language models (LLMs) for complex information tasks like academic research or planning a move to another city. However, while they often require working in a nonlinear manner -- e.g., to arrange information spatially to organize and make sense of it, current interfaces for interacting with LLMs are generally linear to support conversational interaction. To address this limitation and explore how we can support LLM-powered exploration and sensemaking, we developed Sensecape, an interactive system designed to support complex information tasks with an LLM by enabling users to (1) manage the complexity of information through multilevel abstraction and (2) seamlessly switch between foraging and sensemaking. Our within-subject user study reveals that Sensecape empowers users to explore more topics and structure their knowledge hierarchically, thanks to the externalization of levels of abstraction. We contribute implications for LLM-based workflows and interfaces for information tasks.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules of cascaded convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN architectures such as the U-Net model with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed Attention U-Net architecture is evaluated on two large CT abdominal datasets for multi-class image segmentation. Experimental results show that AGs consistently improve the prediction performance of U-Net across different datasets and training sizes while preserving computational efficiency. The code for the proposed architecture is publicly available.
State-of-the-art Convolutional Neural Network (CNN) benefits a lot from multi-task learning (MTL), which learns multiple related tasks simultaneously to obtain shared or mutually related representations for different tasks. The most widely-used MTL CNN structure is based on an empirical or heuristic split on a specific layer (e.g., the last convolutional layer) to minimize different task-specific losses. However, this heuristic sharing/splitting strategy may be harmful to the final performance of one or multiple tasks. In this paper, we propose a novel CNN structure for MTL, which enables automatic feature fusing at every layer. Specifically, we first concatenate features from different tasks according to their channel dimension, and then formulate the feature fusing problem as discriminative dimensionality reduction. We show that this discriminative dimensionality reduction can be done by 1x1 Convolution, Batch Normalization, and Weight Decay in one CNN, which we refer to as Neural Discriminative Dimensionality Reduction (NDDR). We perform ablation analysis in details for different configurations in training the network. The experiments carried out on different network structures and different task sets demonstrate the promising performance and desirable generalizability of our proposed method.
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