Related papers: Confidence Sets in Time-Series Filtering
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$…
A physical data (such as astrophysical, geophysical, meteorological etc.) may appear as an output of an experiment or it may come out as a signal from a dynamical system or it may contain some sociological, economic or biological…
In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…
The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
Time series classification is a task that aims at classifying chronological data. It is used in a diverse range of domains such as meteorology, medicine and physics. In the last decade, many algorithms have been built to perform this task…
The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the…
Digital signals are complex-valued functions on $\Z_n$. Signal sets with certain properties are required in various communication systems. Traditional signal sets consider only the time distortion during transmission. Recently, signal sets…
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…
The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…
Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human…
Stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability…
Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to…