Related papers: Nonlinear Principal Components and Long-run Implic…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
Envelope methods offer targeted dimension reduction for various models. The overarching goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope.…
We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this…
We modify the NonLinear Guiding Center (NLGC) theory (Matthaeus et al. 2003) for perpendicular diffusion by replacing the spectral amplitude of the two-component model magnetic turbulence with the 2D component one (following Shalchi 2006),…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. Continuation MPC, suggested by T.~Ohtsuka in 2004, uses…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…