Related papers: Linear Prediction of Long-Range Dependent Time Ser…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
In this paper we study different approaches for time series modeling. The forecasting approaches using linear models, ARIMA alpgorithm, XGBoost machine learning algorithm are described. Results of different model combinations are shown. For…
In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history…
We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact…
In the 1940s, Wiener introduced a linear predictor, where the future prediction is computed by linearly combining the past data. A transformer generalizes this idea: it is a nonlinear predictor where the next-token prediction is computed by…
As industrial systems become more complex and monitoring sensors for everything from surveillance to our health become more ubiquitous, multivariate time series prediction is taking an important place in the smooth-running of our society. A…
Quantifying predictive uncertainty of deep semantic segmentation networks is essential in safety-critical tasks. In applications like autonomous driving, where video data is available, convolutional long short-term memory networks are…
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…
We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in…
This paper is based on a machine learning project at the Norwegian University of Science and Technology, fall 2020. The project was initiated with a literature review on the latest developments within time-series forecasting methods in the…
Accurate time series prediction is challenging due to the inherent nonlinearity and sensitivity to initial conditions. We propose a novel approach that enhances neural network predictions through differential learning, which involves…
We present Timer-XL, a causal Transformer for unified time series forecasting. To uniformly predict multidimensional time series, we generalize next token prediction, predominantly adopted for 1D token sequences, to multivariate next token…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating…
Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold…
A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise,…
Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such…
Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the…
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…
Over the past several decades, many different types of computational imaging approaches have been proposed for improving MRI. In this paper, we provide an overview of methods that assume that MRI Fourier data is linearly predictable. Linear…