Study identifies Markov chain model parameters from small assortments.
problem Identifying parameters of Markov chain choice models from large assortments.
method Simple and efficient algorithm to recover parameters from assortments of sizes two and three.
result Parameters of the Markov chain choice model can be identified from assortments of sizes two and three.
As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Cha…
Proposes new methods for Markov chain choice models with panel data.
problem Dependence among transactions for the same customer in historical data.
method Expectation-maximization (EM) algorithms incorporating partial-ordering preference information.
result EM algorithms outperform traditional methods on synthetic and real datasets.
Paper generalizes Markov chain model to handle dynamic preferences and choice overload.
problem Modeling dynamic customer substitution behavior in assortment optimization.
method Generalizes Markov chain model to account for choice overload.
result Proposes a Markov chain model that reduces to a generalized MNL model with assortment-dependent no-purchase attractions.
Optimizes control of hybrid systems with multiple switching processes.
problem Optimal control of hybrid systems with multiple Markov switching processes.
method Combines two separate Markov chains into one synthetic chain, derives HJB equations, and solves the portfolio choice problem.
result Derives explicit solutions and value functions for the optimal control problem.
PCMC-Net uses neural networks to estimate transition rates in choice models, improving accuracy over traditional methods.
problem Inference limitations of traditional PCMC models when examples are scarce or new alternatives are observed.
method Amortized inference approach embedding PCMC definition into a neural network.
result Neural network outperforms feature engineered and machine learning models in airline booking prediction.
This paper introduces a new method for optimizing large-scale problems using Markov chain block updates.
problem Optimizing large-scale problems with efficient and natural block selection.
method Markov chain block coordinate descent (BCD) for optimization.
result The method converges for minimizing Lipschitz differentiable functions, with sublinear and linear convergence rates for convex and strongly convex functions, respectively.
First DP MCMC algorithm for arbitrary models.
problem Privacy-preserving Bayesian inference in arbitrary models.
method Decomposition of Barker acceptance test for Rényi DP privacy cost.
result First general DP MCMC algorithm with improved privacy guarantees.
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 inference is often intractable. Markov chain Monte Carlo techniques make approximat…
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.
Algorithm selects optimal experiments in Markov chains to learn unknown quantities.
problem Designing efficient experiments in Markov chains to learn about unknown quantities.
method Proposes extsc{markov-design} algorithm for sequential policy selection.
result Algorithm provably converges to optimal measurement allocation.
Bayesian neural networks' performance varies with prior choice, affecting their ability to identify unknowns.
problem The impact of prior choice on Bayesian neural networks' ability to identify unknowns.
method Evaluation of different prior distributions on classification tasks using BNNs and NNs with Monte Carlo dropout.
result Prior choice significantly impacts BNNs' ability to identify unknowns, affecting true and false positive rates.
In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular…
The study uses Markov chains to forecast cryptocurrency market dynamics.
problem Forecasting and understanding market fluctuations in cryptocurrencies.
method Markov chains of orders one to eight were used to forecast intra-day returns of three major cryptocurrencies.
result Predictions from empirical probabilities outperform random choices.
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
In this paper we describe three stochastic models based on a semi-Markov chains approach and its generalizations to study the high frequency price dynamics of traded stocks. The three models are: a simple semi-Markov chain model, an indexed semi-Markov chain model and a weighted indexed semi-Markov chain model. We show…
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
The paper analyzes learning rates for non-irreducible Markov chains.
problem Real-world data often violates i.i.d. assumptions.
method Examines iterated random functions and contractive functions.
result Derives data-distribution dependent learning rates.
Elo ratings learn model parameters quickly using Markov chains.
problem Ranking players in online settings.
method Bradley--Terry--Luce model and Markov chain theory.
result Elo learns model parameters at a competitive rate.
Improved VAEs by using undirected graphical models as approximate posteriors.
problem Mismatch between approximate and true posterior in VAEs.
method Trained undirected graphical models using backpropagation through Markov chain Monte Carlo updates.
result Undirected models outperform directed models in VAEs.
This paper models time-series data with a mixture of Markov chains, automatically determining the number of components.
problem Tackles the inability of common Markov state modeling frameworks to discern heterogeneities in complex data.
method Uses a mixture of Markov chains and variational expectation-maximization algorithm for automatic component selection.
result Achieves performance consistent with theoretically optimal error scaling, identifying meaningful heterogeneities in various data sets.
This study evaluates different normalizing flow architectures for MCMC.
problem Lack of systematic comparison of normalizing flow architectures in MCMC.
method Extensive evaluation of various normalizing flow architectures on different MCMC methods and target distributions.
result Contractive residual flows are the best general-purpose models for MCMC.
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…
New method improves convergence of gradient descent for non-convex, non-reversible Markov chains.
problem Improving convergence of gradient descent for non-convex, non-reversible Markov chains.
method Introducing a new technique that varies the mixing levels of the Markov chains to establish non-ergodic convergence under wider step sizes.
result Established non-ergodic convergence for non-convex problems and non-reversible finite-state Markov chains.
Improved Metropolized HMC mixing time with multi-step gradients.
problem Improving the efficiency of sampling from complex probability distributions.
method Analyzing Metropolized HMC with multi-step integrators and applying sharpening techniques.
result Non-asymptotic upper bound on mixing time for Metropolized HMC with explicit step-size and leapfrog steps.
Model estimates loan cure rate using Markov chains.
problem Estimating the cure rate of non-performing loans.
method Developed a Markov-chain model for portfolios.
result Efficient and accessible for smaller institutions.
One of the most popular copulas for modeling dependence structures is t-copula. Recently the grouped t-copula was generalized to allow each group to have one member only, so that a priori grouping is not required and the dependence modeling is more flexible. This paper describes a Markov chain Monte Carlo (MCMC) method…
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.
Paper proposes a new method to avoid overfitting in Bayesian network models.
problem Overfitting in Bayesian network models with limited data.
method Uses Monte Carlo Markov chain model choice (MC3) to learn and present reasonably supported networks.
result Flexible structural MC3 method reduces overfitting and presents all possible arcs with their support.
Paper proposes semi-supervised learning with triplet Markov chains.
problem Lack of labels in training data.
method Variational Bayesian inference for semi-supervised learning.
result Derives semi-supervised algorithms for various sequential models.
Method reconstructs hidden Markov chains from insurance data.
problem Recovering hidden Markov chains from incomplete insurance data.
method Neural architecture to explicitly provide transition probabilities.
result Neural model successfully validates decompression of insurance information.
Modified neural network models Markov Chains for non-deterministic outcomes.
problem Simulating non-deterministic behavior in neural networks.
method Developed a modified neural network model capable of simulating Markov Chains.
result Demonstrated the network's ability to produce non-deterministic outcomes.
Hidden Markov Chains and Linear-chain CRFs are equivalent.
problem Comparing Hidden Markov Chains and Conditional Random Fields.
method Constructing an HMC with the same posterior distribution as a CRF.
result HMCs and linear-chain CRFs are equivalent models.
The paper provides concentration inequalities for Markov chain variance estimators.
problem Estimating the variance of Markov chains with concentration properties.
method Martingale decomposition method for uniformly geometrically ergodic Markov chains.
result Explicit control of the p-th moment of the OBM estimator difference and dependence on p and mixing time.
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…
A low-rank tensor model simplifies multi-dimensional Markov chains.
problem Simplifying the dynamics of multi-dimensional Markov chains.
method Low-rank tensor decomposition for multi-dimensional state spaces.
result Our tensor model requires fewer parameters and samples than conventional methods.
A new method simulates a lazy version of a Markov chain for empirical inference.
problem Estimating and testing unknown Markov chains with limited data.
method Simulates an α-lazy version of an unknown Markov chain, making it ergodic.
result The pseudo spectral gap can be applied to non-ergodic Markov chains.
RHOMP improves prediction accuracy for user trails.
problem Predicting user actions in web browsing and geolocation.
method Retrospective higher-order Markov process (RHOMP) for sequences of data.
result RHOMP outperforms higher-order Markov chains and other methods in prediction accuracy.
New algorithms improve inference in non-differentiable models.
problem Inference and learning in latent variable models with non-differentiable densities.
method Proximal interacting particle Langevin algorithms (PIPLA).
result Nonasymptotic bounds and effectiveness demonstrated in various models.
Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
New method adds user constraints to Markov chains for better data reduction.
problem No systematic framework to impose user-defined constraints on Markov chains.
method Path entropy maximization to derive transition probabilities with user constraints.
result Improved nonlinear dimensionality reduction with user-prescribed constraints.
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.
Study shows how certain stochastic models reach a steady state over time.
problem Understanding long-term behavior of stochastic volatility models.
method Novel coupling technique for Markov chains, applicable to random environments.
result Convergence to an invariant measure for multidimensional fractional models.
Study Markov chain gradient descent in Hilbert spaces for quadratic loss.
problem Approximating optimal solutions for quadratic loss functions.
method Developed a Markov chain-based stochastic gradient algorithm in Hilbert spaces.
result Established probabilistic upper bounds on convergence.
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.
A new MCMC method for GPs tackles computational burden and intractable likelihoods.
problem High computational burden and intractable likelihoods in Gaussian process models.
method Combines variationally sparse Gaussian processes with pseudo-marginal MCMC.
result Asymptotically exact inference with computational gains for large datasets.
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
Enhanced Markov chain sampler learns network statistics faster.
problem Learning network statistics efficiently.
method Integrates graph Forman curvature into Markov chain transition probabilities and stationary distribution.
result Curved Markov chain Monte Carlo achieves faster convergence.