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  1. Shoikhet, D. ; Vajiac, E. (Ed.)
    We consider the existence and structure properties of Parseval frames of kernel functions in vector valued de Branges spaces. We develop some sufficient conditions for Parseval sequences by identifying the main construction with Naimark dilation of frames. The dilation occurs by embedding the de Branges space of vector valued functions into a dilated de Branges space of vector valued functions. The embedding also maps the kernel functions associated with a frame sequence of the original space into a Riesz basis for the embedding space. We also develop some sufficient conditions for a dilated de Branges space to have the Kramermore »sampling property.« less
    Free, publicly-accessible full text available May 21, 2023
  2. The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a randomized Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e., the equations within the system are distributed over multiple nodes within a network. The modification we introduce is designed for a network with a tree structure that allows for passage of solution estimates between the nodes in the network. We demonstrate that the algorithm converges to the solution, or the solution of minimal norm, when the system is consistent. We also prove convergence rates of the randomized algorithm that dependmore »on the spectral data of the coefficient matrix and the random control probability distribution. In addition, we demonstrate that the randomized algorithm can be used to identify anomalies in the system of equations when the measurements are perturbed by large, sparse noise.« less
    Free, publicly-accessible full text available March 1, 2023
  3. Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.
    Free, publicly-accessible full text available January 1, 2023
  4. Free, publicly-accessible full text available December 1, 2022
  5. In recent years, many incidents have been reported where machine learning models exhibited discrimination among people based on race, sex, age, etc. Research has been conducted to measure and mitigate unfairness in machine learning models. For a machine learning task, it is a common practice to build a pipeline that includes an ordered set of data preprocessing stages followed by a classifier. However, most of the research on fairness has considered a single classifier based prediction task. What are the fairness impacts of the preprocessing stages in machine learning pipeline? Furthermore, studies showed that often the root cause of unfairnessmore »is ingrained in the data itself, rather than the model. But no research has been conducted to measure the unfairness caused by a specific transformation made in the data preprocessing stage. In this paper, we introduced the causal method of fairness to reason about the fairness impact of data preprocessing stages in ML pipeline. We leveraged existing metrics to define the fairness measures of the stages. Then we conducted a detailed fairness evaluation of the preprocessing stages in 37 pipelines collected from three different sources. Our results show that certain data transformers are causing the model to exhibit unfairness. We identified a number of fairness patterns in several categories of data transformers. Finally, we showed how the local fairness of a preprocessing stage composes in the global fairness of the pipeline. We used the fairness composition to choose appropriate downstream transformer that mitigates unfairness in the machine learning pipeline.« less
    Free, publicly-accessible full text available August 23, 2022
  6. High-throughput phenotyping enables the efficient collection of plant trait data at scale. One example involves using imaging systems over key phases of a crop growing season. Although the resulting images provide rich data for statistical analyses of plant phenotypes, image processing for trait extraction is required as a prerequisite. Current methods for trait extraction are mainly based on supervised learning with human labeled data or semisupervised learning with a mixture of human labeled data and unsupervised data. Unfortunately, preparing a sufficiently large training data is both time and labor-intensive. We describe a self-supervised pipeline (KAT4IA) that uses K -means clusteringmore »on greenhouse images to construct training data for extracting and analyzing plant traits from an image-based field phenotyping system. The KAT4IA pipeline includes these main steps: self-supervised training set construction, plant segmentation from images of field-grown plants, automatic separation of target plants, calculation of plant traits, and functional curve fitting of the extracted traits. To deal with the challenge of separating target plants from noisy backgrounds in field images, we describe a novel approach using row-cuts and column-cuts on images segmented by transform domain neural network learning, which utilizes plant pixels identified from greenhouse images to train a segmentation model for field images. This approach is efficient and does not require human intervention. Our results show that KAT4IA is able to accurately extract plant pixels and estimate plant heights.« less
  7. Diffusion of information in social network has been the focus of intense research in the recent past decades due to its significant impact in shaping public discourse through group/individual influence. Existing research primarily models influence as a binary property of entities: influenced or not influenced. While this is a useful abstraction, it discards the notion of degree of influence, i.e., certain individuals may be influenced ``more'' than others. We introduce the notion of \emph{attitude}, which, as described in social psychology, is the degree by which an entity is influenced by the information. Intuitively, attitude captures the number of distinct neighborsmore »of an entity influencing the latter. We present an information diffusion model (AIC model) that quantifies the degree of influence, i.e., attitude of individuals, in a social network. With this model, we formulate and study attitude maximization problem. We prove that the function for computing attitude is monotonic and sub-modular, and the attitude maximization problem is NP-Hard. We present a greedy algorithm for maximization with an approximation guarantee of $(1-1/e)$. In the context of AIC model, we study two problems, with the aim to investigate the scenarios where attaining individuals with high attitude is objectively more important than maximizing the attitude of the entire network. In the first problem, we introduce the notion of \emph{actionable attitude}; intuitively, individuals with actionable attitude are likely to ``act'' on their attained attitude. We show that the function for computing actionable attitude, unlike that for computing attitude, is non-submodular and however is \emph{approximately submodular}. We present approximation algorithm for maximizing actionable attitude in a network. In the second problem, we consider identifying the number of individuals in the network with attitude above a certain value, a threshold. In this context, the function for computing the number of individuals with attitude above a given threshold induced by a seed set is \emph{neither submodular nor supermodular}. We present heuristics for realizing the solution to the problem. We experimentally evaluated our algorithms and studied empirical properties of the attitude of nodes in network such as spatial and value distribution of high attitude nodes.« less
  8. Constraint satisfaction problems (CSP's) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP's and computation of zeroth frequency moments $(F_0)$ for data streams. Our investigations lead us to observe striking similarity in the coremore »techniques employed in the algorithmic frameworks that have evolved separately for model counting and $F_0$ computation. We design a recipe for translation of algorithms developed for $F_0$ estimation to that of model counting, resulting in new algorithms for model counting. We then observe that algorithms in the context of distributed streaming can be transformed to distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framing $F_0$ estimation as a special case of DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields a state-of-the art algorithm for multidimensional range efficient $F_0$ estimation with a simpler analysis.« less