Study on Kyle-Back model with risk aversion and non-Gaussian beliefs.
problem Existence of equilibrium in Kyle's insider trading model.
method Forward-backward system coupled via optimal transport constraint, stochastic representation, well-posedness of solutions.
result Existence and properties of equilibrium for small risk aversion parameter.
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian Processes (GP), and to states represented as a weighted sum of Gaussians. The key attr…
Develops a Gaussian-based message-passing algorithm for noisy matrix completion.
problem Noisy matrix completion problems.
method Gaussian parameterized belief propagation algorithm.
result Advantages over traditional methods in non-Gaussian noise scenarios.
The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the classical central limit theorem (CLT) kicks in. This assumption is often made for mathematical convenience, since it enables SGD to be analyzed as a stochastic diff…
Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.
problem Intractable likelihoods in Bayesian inference.
method Generalised Bayesian inference with Stein discrepancy as the loss function.
result Robust generalised posteriors with closed form or accessible using MCMC.
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
Generalized belief propagation converges to optimal solutions on graphs with motifs.
problem Understanding belief propagation on loopy graphs.
method Study of generalized belief propagation on graphs with motifs.
result Generalized belief propagation converges to the global optimum of the Bethe free energy.
Study risk sharing with Lambda VaR under diverse beliefs.
problem Risk sharing among agents with different beliefs.
method Use Lambda Value-at-Risk as preference, analyze under heterogeneous beliefs.
result Explicit formulas for risk sharing under various belief scenarios.
Belief propagation recovers backpropagation results.
problem Connection between backpropagation and belief propagation poorly understood.
method Converted backpropagation input to belief propagation input and showed results.
result Backpropagation is a special case of belief propagation.
New framework analyzes belief evolution in social networks.
problem Analyzing belief evolution in social networks.
method Proposes a new theoretical framework using Markov chain theory for horizontal and vertical transmission.
result Homophily-based networks do not converge to a single set of beliefs.
We consider the problem of imitation learning from expert demonstrations in partially observable Markov decision processes (POMDPs). Belief representations, which characterize the distribution over the latent states in a POMDP, have been modeled using recurrent neural networks and probabilistic latent variable models, …
The paper analyzes the non-Gaussian behavior of inflation and unemployment over 70 years using multifractal methods.
problem Capturing unusual fluctuations in inflation and unemployment over long periods.
method Coupled multifractal approach to analyze non-Gaussian distributions of inflation and unemployment over 70 years.
result The non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year, while inflation's non-Gaussianity persists across all time scales.
The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made for mathematical convenience, since it enables SGD to be analyzed as a stochast…
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
Improved error correction using neural networks and belief propagation.
problem Inference in factor graphs with loops or poor approximations.
method Hybrid model combining FG-GNN and belief propagation.
result Hybrid model outperforms belief propagation in error correction tasks.
NBF combines deep learning with classical filtering for better belief tracking.
problem Maintaining distributions over hidden states in partially observable systems.
method Trains neural networks to map beliefs to fixed-length vectors, updating them with incoming observations and dynamics.
result NBF efficiently tracks shifting, multimodal beliefs without particle impoverishment.
This thesis investigates belief propagation's performance in graphical models with loops.
problem Belief propagation's performance and convergence guarantees in models with loops are uncertain.
method Investigates how model parameters affect belief propagation's performance, convergence, and approximation quality.
result Model parameters influence the number of fixed points, convergence properties, and approximation quality of belief propagation.
FORBES learns flexible belief states for POMDPs using normalizing flows.
problem Accurately modeling belief states in POMDPs for high-dimensional, continuous spaces.
method Integrates normalizing flows into variational inference for continuous belief state learning.
result FORBES learns flexible belief states that enable multi-modal predictions and high-quality reconstructions.
This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an N-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents…
Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful in practice, even though its empirical success, typically, lacks theoretical gu…
Model captures decision-making under bounded rationality with prior beliefs and market feedback.
problem Bounded rationality in decision-making with limited processing abilities.
method Maximum entropy principle applied to Quantal Response Statistical Equilibrium framework.
result Prior beliefs influence decision-making, altering the outcome of market feedback.
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires n≳d4 samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches n≳d2. By elaborating on the notion of linear belief functions (Dempster 1990; Liu 1996), we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show how to use basic matrices to represent market information and financial knowledge, including complete ignorance, stat…
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace E in Rn so that data points projected onto E follow a non-gaussian distribution. Although this is an appropriate model for some real world data analysis problems, there has been little progress on t…
This paper optimizes reinsurance contracts with belief differences between insurer and reinsurer.
problem Dynamic reinsurance design with heterogeneous beliefs under mean-variance framework.
method Modeling surplus process, applying partitioned domain optimization, solving HJB system.
result Optimal reinsurance contracts with belief heterogeneity are more complex than standard contracts.
Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single…
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.
In this paper I empirically investigate prediction markets for binary options. Advocates of prediction markets have suggested that asset prices are consistent estimators of the "true" probability of a state of the world being realized. I test whether the market reaches a "consensus." I find little evidence for converge…
New algorithm reduces communication in distributed learning by sharing compressed beliefs.
problem Efficiently learning from private data in a distributed setting with large hypothesis sets.
method Proposes a belief update rule for distributed cooperative learning with compressed (sparse or quantized) beliefs.
result Beliefs converge almost surely to optimal hypotheses with a linear concentration rate.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
New α-BP algorithm improves belief propagation for graphs with loops.
problem Uncertainty in belief propagation for graphs with loops.
method Derive α-BP algorithm motivated by minimizing α-divergence. result Proves convergence conditions for α-BP. New group testing method uses Belief Propagation for accurate screening.
problem Efficiently identifying infected samples in large groups with minimal tests.
method Belief Propagation algorithm for inference in group testing schemes.
result Significantly increased accuracy of infection identification with fewer tests.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
A new vine copula mixture model improves clustering accuracy for non-Gaussian data.
problem Finite mixture models struggle with asymmetric tail dependencies and non-elliptical clusters.
method Proposes a vine copula mixture model for clustering non-Gaussian data, addressing model selection and parameter estimation.
result Significant improvement in clustering accuracy for data with asymmetric tail dependencies or non-Gaussian margins.
Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is actually minimization of a localized α-divergence. We term this algorithm as $α…
Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinit…
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
Paper solves NGCA for discrete distributions using LLL method.
problem Learning hidden non-Gaussian components in discrete distributions.
method Utilizes LLL lattice basis reduction method.
result Sample and computationally efficient algorithm for NGCA in discrete distributions.
The paper explains stock market predictability through a model of heterogeneous beliefs.
problem Understanding and predicting stock market behavior based on news and investor beliefs.
method A discrete-time model of heterogeneous beliefs where some agents receive noisy signals about asset fundamentals.
result Momentum and reversal in stock prices arise from investors' incorrect beliefs about signal accuracy and fundamental values.
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such marginals when the underlying graph is a tree. But it has gained its popularity as …
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Algorithm learns non-Gaussian graphical models via Hessian scores and triangular transport.
problem Learning graph structure from non-Gaussian data.
method Score based on integrated Hessian information, coupled with triangular transport map.
result Algorithm successfully recovers graph structure for non-Gaussian data.
Study shows price bubbles can exist even with heterogeneous beliefs.
problem Equilibrium price formation in markets with different belief groups.
method Analyzes continuous time asset trading with heterogeneous investors and mean reverting asset.
result Price bubbles may not form even with heterogeneous beliefs, contrary to initial expectations.
A method for eliciting expert beliefs using preferential questions and normalizing flows.
problem Eliciting high-dimensional probability distributions from noisy judgments.
method Normalizing flows based on preferential questions with a novel functional prior.
result The method allows for the inference of arbitrarily flexible densities from preferential judgments.
Develops a framework for quantifying agentic AI model risk using LLM-inferred Bayesian state filters.
problem Quantifying the risk of agentic AI systems due to uncertain beliefs and actions.
method Representing the system as a partially observed Markov decision process with latent states, Bayesian belief updates, control-dependent losses, and tail-risk functionals.
result Develops a rigorous framework for separating uncertainty quantification from risk measurement.
The paper examines non-Gaussian models for financial data.
problem Modeling financial data with non-Gaussian distributions.
method Analysis of multivariate non-Gaussian models focusing on parsimony, dependence structure, and computational aspects.
result Characterization and calibration of models for financial log-returns.