Related papers: The application of computational mechanics to the …

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…

We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…

Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…

Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…

Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…

We investigate the possibility of using Gaussian process regression to smooth data on the current past null-cone for use as the input to a relativistic integration scheme. The algorithm we present is designed to reconstruct the metric of…

Real-world multivariate time series, particularly in critical infrastructure such as electrical power grids, are often corrupted by noise and anomalies that degrade the performance of downstream tasks. Standard data cleaning approaches…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…

This paper considers a noisy data structure recovery problem. The goal is to investigate the following question: Given a noisy observation of a permuted data set, according to which permutation was the original data sorted? The focus is on…

The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…

The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar…

The assumption of separability is a simplifying and very popular assumption in the analysis of spatio-temporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for…

Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e.g., non-affine,…

Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between…

Quantum machine learning uses principles from quantum mechanics to process data, offering potential advances in speed and performance. However, previous work has shown that these models are susceptible to attacks that manipulate input data…

The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…