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We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could…
Multivariate time series have many applications, from healthcare and meteorology to life science. Although deep learning models have shown excellent predictive performance for time series, they have been criticised for being "black-boxes"…
Time series forecasting drives operational decisions in areas like finance, transportation, and energy. While supervised learning approaches achieve strong performance, they require domain-specific training, feature engineering, and ongoing…
The forecasting problem for a stationary and ergodic binary time series $\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ based on the observations $X_i$, $0\le i\le n$ without prior knowledge of the distribution of…
Deep learning time-series models are often used to make forecasts that inform downstream decisions. Since these decisions can differ from those in the training set, there is an implicit requirement that time-series models will generalize…
With the advancement of GPS and remote sensing technologies, large amounts of geospatial and spatiotemporal data are being collected from various domains, driving the need for effective and efficient prediction methods. Given spatial data…
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
We present a conformal prediction method for time series using the Transformer architecture to capture long-memory and long-range dependencies. Specifically, we use the Transformer decoder as a conditional quantile estimator to predict the…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…
In Das and Politis(2020), a model-free bootstrap(MFB) paradigm was proposed for generating prediction intervals of univariate, (locally) stationary time series. Theoretical guarantees for this algorithm was resolved in Wang and…
Various verification techniques for temporal properties transform temporal verification to safety verification. For infinite-state systems, these transformations are inherently imprecise. That is, for some instances, the temporal property…
We state and prove a theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of stationary population identity. Applications of this theorem for practical…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional…
Research at the intersection of machine learning and the social sciences has provided critical new insights into social behavior. At the same time, a variety of critiques have been raised ranging from technical issues with the data used and…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…