Related papers: Beyond Gaussian Assumptions: A Nonlinear Generaliz…

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

Langevin models are frequently used to model various stochastic processes in different fields of natural and social sciences. They are adapted to measured data by estimation techniques such as maximum likelihood estimation, Markov chain…

We consider to learn a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…

We present detailed theoretical model of electron motion inside of an atom or molecule when subjected to electro-magnetic wave. This theoretical model, that we called Invicem Lorentz Oscillator Model (ILOM), contains Lorentz Oscillator…

Line-intensity mapping (LIM) is quickly attracting attention as an alternative technique to probe large-scale structure and galaxy formation and evolution at high redshift. LIM one-point statistics are motivated because they provide access…

Line-intensity mapping (LIM) is an emerging cosmological technique that traces large-scale structure through the integrated spectral-line emission of unresolved sources. Reconstructing unbiased sky maps requires careful joint treatment of…

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and…

This paper presents normalizing flows for incremental smoothing and mapping (NF-iSAM), a novel algorithm for inferring the full posterior distribution in SLAM problems with nonlinear measurement models and non-Gaussian factors. NF-iSAM…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

In nature, active inference agents must learn how observations of the world represent the state of the agent. In engineering, the physics behind sensors is often known reasonably accurately and measurement functions can be incorporated into…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

Latent force models (LFMs) are flexible models that combine mechanistic modelling principles (i.e., physical models) with non-parametric data-driven components. Several key applications of LFMs need non-linearities, which results in…