Related papers: Analysing symbolic data by pseudo-marginal methods
This study investigates the use of symbolic computation in Matrix Structural Analysis (MSA) for continuous beams, leveraging the MATLAB Symbolic Math Toolbox. By employing symbolic MSA, analytical expressions for displacements, support…
Multi-state survival analysis (MSA) uses multi-state models for the analysis of time-to-event data. In medical applications, MSA can provide insights about the complex disease progression in patients. A key challenge in MSA is the accurate…
Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…
Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…
Stacked denoising autoencoders (SDAs) have been successfully used to learn new representations for domain adaptation. Recently, they have attained record accuracy on standard benchmark tasks of sentiment analysis across different text…
This paper applies probabilistic model checking techniques for discrete Markov chains to inference in Bayesian networks. We present a simple translation from Bayesian networks into tree-like Markov chains such that inference can be reduced…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Bayesian inference for spatial point patterns is often hindered computationally by intractable likelihoods. In the frequentist literature, estimating equations utilizing pseudolikelihoods have long been used for simulation-free parameter…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…
Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…
Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…
Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…
Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…