Related papers: Discrete Signal Processing with Set Functions
A rigorous formulation of the dynamics of a signal processing scheme aimed at dense signal scanning without any loss in accuracy is introduced and analyzed. Related methods proposed in the recent past lack a satisfactory analysis of whether…
Partition selection, or set union, is an important primitive in differentially private mechanism design: in a database where each user contributes a list of items, the goal is to publish as many of these items as possible under differential…
We study sublevel set and superlevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. Finite ordered sets also serve as the codomain of our…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
We study the basic operation of set union in the global model of differential privacy. In this problem, we are given a universe $U$ of items, possibly of infinite size, and a database $D$ of users. Each user $i$ contributes a subset $W_i…
Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional…
We study the problem of designing models for machine learning tasks defined on \emph{sets}. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to…
Neural processes (NPs) aim to stochastically complete unseen data points based on a given context dataset. NPs essentially leverage a given dataset as a context representation to derive a suitable identifier for a novel task. To improve the…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
Node classification is a central task in relational learning, with the current state-of-the-art hinging on two key principles: (i) predictions are permutation-invariant to the ordering of a node's neighbors, and (ii) predictions are a…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…
Recent progress in semantic segmentation has been driven by improving the spatial resolution under Fully Convolutional Networks (FCNs). To address this problem, we propose a Stacked Deconvolutional Network (SDN) for semantic segmentation.…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We…