Related papers: Prediction Theory for Stationary Functional Time S…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
This paper discusses desirable properties of forecasting models in production systems. It then develops a family of models which are designed to satisfy these properties: highly customizable to capture complex patterns; accommodates a large…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…
Time-series classification is an important domain of machine learning and a plethora of methods have been developed for the task. In comparison to existing approaches, this study presents a novel method which decomposes a time-series…
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are…
We introduce a neural network conformal prediction method for time series that enhances adaptivity in non-stationary environments. Our approach acts as a neural controller designed to achieve desired target coverage, leveraging auxiliary…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…
Precision predictions combined with precise measurements are a major tool in sharpening our understanding of the fundamental laws underlying microscopic as well as macroscopic systems. Here, I present a few remarkable examples covering the…
Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…
We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets,…