Study compares three schemes for solving complex control problems, finding scheme (i) problematic.
problem Solving Hamilton-Jacobi-Bellman quasi-variational inequalities for combined stochastic and impulse control problems.
method Direct, penalized, and semi-Lagrangian discretization schemes; use of weakly chained diagonally dominant matrices.
result Policy iteration convergence conditions and comparison of schemes; scheme (i) not recommended.
Study nonparametric estimator for Markov chain transition matrices in offline setting.
problem Estimating transition matrices of finite controlled Markov chains from logged data.
method Developed sample complexity bounds and conditions for minimaxity.
result Achieving certain statistical risk requires balancing mixing properties and sample size.
The paper improves generalization bounds for classifier chains with interdependent labels.
problem Improving generalization for classifier chains with multiple interdependent labels.
method Using large deviation inequalities for weakly dependent sequences, the paper derives a new generalization error bound.
result The derived bound explicitly shows dependencies between class labels and provides insights into the chain's order.
Algorithm learns transition matrices of multiple unknown Markov chains.
problem Learning transition matrices of multiple unknown Markov chains.
method Adaptive allocation of Markov chains for sequential learning.
result Algorithm efficiently balances exploration and exploitation, achieving optimal asymptotic loss.
Paper introduces MSA for weakly supervised covariance alignment in MEG signals.
problem Limited labeled signals in target datasets for MEG applications.
method Mixing model Stiefel Adaptation (MSA) leveraging unlabeled data.
result MSA outperforms recent methods in brain-age regression with MEG signals.
A theorem simplifies mass-minimizing flat chains' regularity.
problem Understanding the regularity of mass-minimizing flat chains.
method Simple condition for fundamental regularity principle.
result Fundamental regularity principle holds for mass-minimizing chains.
Study LASSO for high-dimensional VAR models with weakly dependent innovations.
problem Understanding sparse regularization in high-dimensional VAR models with weakly dependent innovations.
method LASSO estimation for weakly sparse VAR models with heavy tailed innovations, under L1 mixingale condition. result Oracle properties of LASSO estimation in high-dimensional VAR models with weakly dependent innovations.
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
Matrix Chernoff bound for Markov chains applied to co-occurrence matrices.
problem Analyzing the behavior of co-occurrence statistics in sequential data.
method Proved a matrix Chernoff-type bound for sums of matrix-valued random variables sampled via a regular Markov chain.
result Achieved exponentially fast convergence rate and sample complexity analysis for co-occurrence matrices.
The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub-)linear functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio-Kirchhei…
Improved Bayesian regression for large datasets using multilevel Gibbs sampling.
problem Efficiently handling large-scale Bayesian regression with complex posterior distributions.
method Developed a multilevel Gibbs sampler for linear mixed models, incorporating data clustering and correlated samples for variance reduction.
result Significant speed-up achieved for Bayesian regression without sacrificing predictive performance.
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which cover all elliptic, overdetermined elliptic, subelliptic and parabolic…
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
Market makers optimize bid/ask quotes under hidden Markov chain uncertainty.
problem Optimizing market quotes with hidden factors affecting order intensities.
method Solves stochastic control problem using filtering, control, and PDMPs theory.
result Value function is unique viscosity solution of dynamic programming equation.
Study approximates financial market with discrete-time models.
problem Approximating continuous-time financial market models with discrete-time.
method Constructs discrete-time market models with Markov switching and proves convergence.
result Discrete-time models converge to continuous-time Black-Scholes model with Markov switching.
This paper proposes a stochastic model using the concept of Markov chains for the inter-state transitions of the millisecond order quasi-stable phase synchronized patterns or synchrostates, found in multi-channel Electroencephalogram (EEG) signals. First and second order transition probability matrices are estimated fo…
Constructs manifolds from quantum codes with novel geometric properties.
problem Creating manifolds with specific geometric constraints.
method Reverse engineering manifolds from quantum code chain complexes.
result First examples of power law Z2 systolic freedom. Paper shows structured random matrices can reduce high-dimensional sets to lower dimensions efficiently.
problem Dimensionality reduction of general sets.
method Using structured random matrices and chaining argument to connect to sparse vectors.
result Near optimal distortion embedding of any set into lower dimensions.
The paper proves a dense geodesic in a specific space related to group theory.
problem Existence of a dense geodesic in a specific space.
method Using the Lipschitz metric and properties of matrices, the paper proves the existence of a dense geodesic.
result A dense geodesic is proven in the Out(Fr)-quotient of reduced Outer Space. Estimates covariance matrices using Markov chain Monte Carlo with improved sample complexity.
problem Complexity of covariance matrix estimation for Gibbs distributions.
method Uses Markov chain Monte Carlo with conditions on the chain's spectral gap and Poincaré inequality.
result Achieves similar sample complexity as i.i.d. samples with better query complexity.
Optimal sequential testing for Markovian data with lower and upper bounds.
problem Sequential hypothesis testing for Markovian data.
method Non-asymptotic lower bounds and optimal test design.
result Optimal test matches lower bound asymptotically.
U-turn chains improve sampling from complex distributions.
problem Sampling from high-dimensional learned distributions.
method Iterative forward-backward diffusion steps with Metropolis-Hastings correction.
result Minimal U-turn dynamics exhibit phase transitions and layer-ordering inversion.
Identity testing for reversible Markov chains without symmetry assumption.
problem Identity testing of reversible Markov chains.
method Using distance notion from Daskalakis et al. [2018a], testing without symmetry assumption.
result It is possible to perform identity testing under weaker assumption of reversibility.
Improved machine learning performance through structured random orthogonal embeddings.
problem Improving accuracy and speed in machine learning applications.
method Structured random orthogonal matrices for dimensionality reduction and kernel approximation.
result Significant improvement in accuracy and speed compared to existing methods.
Enhances sample diversity in SGMCMC for better uncertainty estimation in BNNs.
problem Limited sample diversity in SGMCMC affects uncertainty estimation and model performance.
method Reparameterizes neural network weights to produce a more diverse set of samples.
result The proposed approach achieves superior performance in image classification tasks, including OOD robustness.
New method estimates sparse covariance matrices in logit mixtures.
problem Estimating correlations among random coefficients in logit models.
method Mixed-integer optimization (MIO) with Markov Chain Monte Carlo (MCMC) for posterior draws.
result Correctly recovers true covariance structure from synthetic data.
Develops CLTs for Markov chain transition probabilities and policies.
problem Estimating transition probabilities and policies in controlled Markov chains.
method Non-parametric estimator for transition matrices; CLTs for value, Q-, and advantage functions; goodness-of-fit tests.
result Asymptotic normality of estimators under specific logging policies.
Study reveals weak knotting in confined polymers, not dominated by any single knot type.
problem Characterizing knotting in open, confined polymers.
method Modeling open curves as virtual knots, comparing lattice walks and ideal chains in confined and unconfined conditions.
result Weak knotting is a common feature in confined polymers, not dominated by any single knot type.
DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.
problem Efficiently integrate trajectory and snapshot time series data.
method Reformulate DDD to use compact basis functions, reducing parameter scaling.
result Inference of sparse matrices reduces the number of parameters in DDD.
Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.
problem Challenges in high-dimensional generalized tensor bandits where existing algorithms fail.
method Proposes a generalized linear tensor bandits algorithm with a unified analytical framework using convex optimization and weakly decomposable regularizers.
result Unified analytical framework provides better bounds and broader applicability compared to existing methods.
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given representation, constitutes the subject of a separate, ulterior report. The appendix of the p…
Paper develops a method to approximate Markov chains with fewer states.
problem Identifying the state aggregation structure of Markov chains with fewer states.
method Proposes a convex optimization problem with a nonnegative factorization approach.
result The method likely converges to the global solution and outperforms existing methods.
The study examines convergence of stochastic processes on large graphs and adjacency matrices.
problem Analyzing convergence of stochastic processes on large graphs and adjacency matrices.
method Introduced new metrics on the space of measure-valued graphons and used them to show convergence of random trajectories to deterministic curves.
result The Metropolis chain converges to a deterministic gradient flow curve on the space of graphons under certain conditions.
Researchers discovered geodesics and shortest arcs on SL(2) Lie group.
problem Finding shortest paths on a specific Lie group.
method Left-invariant sub-Riemannian metric analysis.
result Geodesics and shortest arcs identified on SL(2). Estimates transition rates of continuous-time Markov chains using imprecise probabilistic methods.
problem Estimating transition rate matrix from a finite-duration process.
method Imprecise probabilistic framework with conjugate priors and discrete-time analysis for hyperparameter determination.
result Continuous-time estimator with simple closed-form expression derived from discrete-time model.
Method estimates number of clusters in Block Markov Chain trajectories.
problem Challenges in choosing number of clusters for sequential data.
method Spectral embedding and density-based clustering.
result Asymptotically consistent method for estimating clusters.
Edge subdivision affects the Perron eigenvalue of tree Ricci matrices.
problem Understanding how edge subdivision impacts the Perron eigenvalue of tree Ricci matrices.
method Compressing branches into scalar feedback functions via Schur complement, reducing the spectral problem to a one-dimensional Chebyshev equation.
result Edge subdivision can decrease, preserve, or increase the Perron eigenvalue of tree Ricci matrices.
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
problem Slow convergence of Krylov subspace solvers for ill-conditioned matrices.
method Graph neural surrogate and Bayesian optimization for AI-tuned MCMC parameters.
result 50% reduction in iterations to convergence on unseen system.
Paper develops a risk scoring framework for tokenized RWA markets.
problem Tokenized assets may not reflect true risk due to illiquidity and concentration.
method Develops a risk scoring framework based on observable indicators.
result Assets with limited transfer activity and concentrated ownership have high empirical risk.
Kernel methods summarize and integrate posterior similarity matrices from Bayesian clustering.
problem Summarizing and integrating posterior similarity matrices from Bayesian clustering.
method Positive semi-definite PSMs, kernel matrices, kernel methods, combining kernels.
result Kernel methods effectively summarize and integrate posterior similarity matrices.
Gradient learning optimises MCMC proposal distributions.
problem Intractable targets in MCMC sampling.
method Gradient-based optimisation of proposal distributions using a maximum entropy regularised objective function.
result Our method can outperform traditional MCMC algorithms, including Hamiltonian Monte Carlo.
Explains a new approach to summarize network data using personalized PageRank matrices.
problem Understanding the essence of sparse and multifaceted network data.
method Develops a new algebraic approach using personalized PageRank matrices.
result Summarizes basic algebraic properties of personalized PageRank matrices.
LEAPS samples discrete distributions via CTMCs and locally equivariant networks.
problem Sampling from discrete distributions with known normalization.
method Continuous-time Markov chain, locally equivariant functions, attention layers, convolutional networks.
result LEAPS minimizes the variance of importance weights, improving sampling efficiency.
A simple framework uses daily prices and volumes to beat the market.
problem Optimizing portfolio performance using only observable data.
method Three matrices derived from price history: return correlations, monthly ranking Markov chains.
result Market-beating portfolio with high Sharpe ratios.
The study analyzes how stochastic recursive algorithms converge to Markov chains.
problem Understanding convergence of stochastic recursive algorithms to Markov chains.
method Analyzes iterated random operators and contraction operators over Polish spaces.
result The distribution of random sequences converges to the invariant distribution of the Markov chain.
Software estimates inequality in random systems with changing communities.
problem Measuring inequality in systems with dynamic interactions and random attributes.
method Piecewise homogeneous Markov chain for changing points, copula function for multivariate distribution, Monte Carlo algorithm for entropy estimation.
result Estimates Random Theil's Entropy to measure inequality in random systems.
A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in Rn with the space of flat m-cochains, that is, the dual space of flat chains of dimension m in Rn. The main purpose of the present paper is to generalize Wolfe's theorem to the se…
Sharp rates found for learning with dependent data, avoiding sample size deflation.
problem Learning with dependent data and square loss.
method Combining weak sub-Gaussian class and mixed tail generic chaining.
result Achieves a rate that only depends on class complexity and second order statistics.