Related papers: UNIPoint: Universally Approximating Point Processe…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…
Neural Processes (NPs) (Garnelo et al 2018a;b) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Modeling event sequences of multiple event types with marked temporal point processes (MTPPs) provides a principled way to uncover governing dynamical rules and predict future events. Current neural network approaches to MTPP inference rely…
We introduce the notion of intensity reweighted moment pseudostationary point processes on linear networks. Based on arbitrary general regular linear network distances, we propose geometrically corrected versions of different higher-order…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We establish fundamental mathematical limits on universal approximation theorem (UAT) system alignment by proving that catastrophic failures are an inescapable feature of any useful computational system. Our central thesis is that for any…
We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all…
Points-to analysis is the problem of approximating run-time values of pointers statically or at compile-time. Points-to sets are used to store the approximated values of pointers during points-to analysis. Memory usage and running time…
The explosion of digital information and the growing involvement of people in social networks led to enormous research activity to develop methods that can extract meaningful information from interaction data. Commonly, interactions are…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in…
Techniques for understanding the functioning of complex machine learning models are becoming increasingly popular, not only to improve the validation process, but also to extract new insights about the data via exploratory analysis. Though…
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…
Continuous-time event sequences, in which events occur at irregular intervals, are ubiquitous across a wide range of industrial and scientific domains. The contemporary modeling paradigm is to treat such data as realizations of a temporal…
We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more.…
A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction…
We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem,…