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Survival Analysis (SA) is about modeling the time for an event of interest to occur, which has important applications in many fields, including medicine, defense, finance, and aerospace. Recent work has demonstrated the benefits of using Neural Networks (NNs) to capture complicated relationships in SA. However, the datasets used to train these models are often subject to uncertainty (e.g., noisy measurements, human error), which we show can substantially degrade the performance of existing techniques. To address this issue, this work leverages recent advances in NN verification to provide new algorithms for generating fully parametric survival models that are robust to such uncertainties. In particular, we introduce a robust loss function for training the models and use CROWN-IBP regularization to address the computational challenges with solving the resulting Min-Max problem. To evaluate the proposed approach, we apply relevant perturbations to publicly available datasets in the SurvSet repository and compare survival models against several baselines. We empirically show that Survival Analysis with Adversarial Regularization (SAWAR) method on average ranks best for dataset perturbations of varying magnitudes on metrics such as Negative Log Likelihood (NegLL), Integrated Brier Score (IBS), and Concordance Index (CI), concluding that adversarial regularization enhances performance in SA. Code: //github.com/mlpotter/SAWAR

Generalization and sample efficiency have been long-standing issues concerning reinforcement learning, and thus the field of Offline Meta-Reinforcement Learning~(OMRL) has gained increasing attention due to its potential of solving a wide range of problems with static and limited offline data. Existing OMRL methods often assume sufficient training tasks and data coverage to apply contrastive learning to extract task representations. However, such assumptions are not applicable in several real-world applications and thus undermine the generalization ability of the representations. In this paper, we consider OMRL with two types of data limitations: limited training tasks and limited behavior diversity and propose a novel algorithm called GENTLE for learning generalizable task representations in the face of data limitations. GENTLE employs Task Auto-Encoder~(TAE), which is an encoder-decoder architecture to extract the characteristics of the tasks. Unlike existing methods, TAE is optimized solely by reconstruction of the state transition and reward, which captures the generative structure of the task models and produces generalizable representations when training tasks are limited. To alleviate the effect of limited behavior diversity, we consistently construct pseudo-transitions to align the data distribution used to train TAE with the data distribution encountered during testing. Empirically, GENTLE significantly outperforms existing OMRL methods on both in-distribution tasks and out-of-distribution tasks across both the given-context protocol and the one-shot protocol.

In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data analysis, and they have been widely used in the area of econometrics. Nevertheless, the non-smoothness of objective functions and constraints present computational challenges for many existing solvers in the presence of ultra-high dimensional covariates. In this paper, we design efficient and parallelizable algorithms for solving sparse SVM problems with high dimensional data through feature space split. The proposed algorithm is based on the alternating direction method of multiplier (ADMM). We establish the rate of convergence of the proposed ADMM method and compare it with existing solvers in various high and ultra-high dimensional settings. The compatibility of the proposed algorithm with parallel computing can further alleviate the storage and scalability limitations of a single machine in large-scale data processing.

The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far less attention given to the effect of memory limitations on performance. Recently, this latter topic has drawn much interest in the engineering and computer science literature. In this survey paper, we attempt to review the state-of-the-art of statistical inference under memory constraints in several canonical problems, including hypothesis testing, parameter estimation, and distribution property testing/estimation. We discuss the main results in this developing field, and by identifying recurrent themes, we extract some fundamental building blocks for algorithmic construction, as well as useful techniques for lower bound derivations.

Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional approximation (MFA) is an innovative data model designed to tackle substantial challenges in scientific data analysis. It computes values and derivatives with high-order accuracy throughout the spatial domain, mitigating artifacts associated with zero- or first-order interpolation. However, the slow query time through MFA makes it less suitable for interactively visualizing a large MFA model. In this work, we develop the first scalable interactive volume visualization pipeline, MFA-DVV, for the MFA model encoded from large-scale datasets. Our method achieves low input latency through distributed architecture, and its performance can be further enhanced by utilizing a compressed MFA model while still maintaining a high-quality rendering result for scientific datasets. We conduct comprehensive experiments to show that MFA-DVV can decrease the input latency and achieve superior visualization results for big scientific data compared with existing approaches.

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. In particular, this class includes very conventional metrics, such as the Euclidean distance or Jeffrery's divergence, as well as a number of other more sophisticated distances recently derived from Riemannian geometry considerations, such as the log-Euclidean metric. In particular, we analyze the asymptotic behavior of this class of functionals by establishing a central limit theorem that allows us to describe their asymptotic statistical law. In order to account for the fact that the sample sizes of two SCMs are of the same order of magnitude as their observation dimension, results are provided by assuming that these parameters grow to infinity while their quotients converge to fixed quantities. Numerical results illustrate how this type of result can be used in order to predict the performance of these metrics in practical machine learning algorithms, such as clustering of SCMs.

The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell (PIC) methods owing to its ease of implementation and favorable scalability in high-dimensional problems. An unfortunate drawback of the method is the introduction of statistical noise resulting from the use of finitely many particles. In this paper we examine the application of the Smoothness-Increasing Accuracy-Conserving (SIAC) family of convolution kernel filters as denoisers for moment data arising from PIC simulations. We show that SIAC filtering is a promising tool to denoise PIC data in the physical space as well as capture the appropriate scales in the Fourier space. Furthermore, we demonstrate how the application of the SIAC technique reduces the amount of information necessary in the computation of quantities of interest in plasma physics such as the Bohm speed.

We study the problem of contextual feature selection, where the goal is to learn a predictive function while identifying subsets of informative features conditioned on specific contexts. Towards this goal, we generalize the recently proposed stochastic gates (STG) Yamada et al. [2020] by modeling the probabilistic gates as conditional Bernoulli variables whose parameters are predicted based on the contextual variables. Our new scheme, termed conditional-STG (c-STG), comprises two networks: a hypernetwork that establishes the mapping between contextual variables and probabilistic feature selection parameters and a prediction network that maps the selected feature to the response variable. Training the two networks simultaneously ensures the comprehensive incorporation of context and feature selection within a unified model. We provide a theoretical analysis to examine several properties of the proposed framework. Importantly, our model leads to improved flexibility and adaptability of feature selection and, therefore, can better capture the nuances and variations in the data. We apply c-STG to simulated and real-world datasets, including healthcare, housing, and neuroscience, and demonstrate that it effectively selects contextually meaningful features, thereby enhancing predictive performance and interpretability.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.