Related papers: Beyond Gaussian Assumptions: A Nonlinear Generaliz…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Regression models are popular tools in empirical sciences to infer the influence of a set of variables onto a dependent variable given an experimental dataset. In neuroscience and cognitive psychology, Generalized Linear Models (GLMs)…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…
Understanding black-box machine learning models is crucial for their widespread adoption. Learning globally interpretable models is one approach, but achieving high performance with them is challenging. An alternative approach is to explain…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
Line intensity mapping (LIM) is an emerging observational method to study the large-scale structure of the Universe and its evolution. LIM does not resolve individual sources but probes the fluctuations of integrated line emissions. A…
In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
Line intensity mapping (LIM) is a rapidly emerging technique for constraining cosmology and galaxy formation using multi-frequency, low angular resolution maps. Many LIM applications crucially rely on cross-correlations of two line…
The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D…
The dynamics of a linear system embedded in a heat bath environment and subject to non- Gaussian noise is studied. Higher order cumulants in coordinate space are derived and their impact on the dynamics and on asymptotic steady state…
Line intensity mapping (LIM) is an emerging technique with a unique potential to probe a wide range of scales and redshifts. Realizing the full potential of LIM, however, relies on accurate modeling of the signal. We introduce an extended…
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
Intensity mapping of the neutral hydrogen brightness temperature promises to provide a three-dimensional view of the universe on very large scales. Nonlinear effects are typically thought to alter only the small-scale power, but we show how…