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…
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48 results for “Markov chain choice models”
This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. Th…
Estimation, Prediction, and Assortment Optimization for Markov Chain Choice Models with Panel Datacs.LG
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.
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.
The method of block coordinate gradient descent (BCD) has been a powerful method for large-scale optimization. This paper considers the BCD method that successively updates a series of blocks selected according to a Markov chain. This kind of block selection is neither i.i.d. random nor cyclic. On the other hand, it is…
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…
Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC)…
Assortment optimization is an important problem that arises in many industries such as retailing and online advertising where the goal is to find a subset of products from a universe of substitutable products which maximize seller's expected revenue. One of the key challenges in this problem is to model the customer su…
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.
Pairwise Choice Markov Chains (PCMC) have been recently introduced to overcome limitations of choice models based on traditional axioms unable to express empirical observations from modern behavior economics like context effects occurring when a choice between two options is altered by adding a third alternative. The i…
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.
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.
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…
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…
Markov Observation Modelsstat.ML
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.
We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a …
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.
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.
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.
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…
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…
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.
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.
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.
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.
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.
Marginal AMP Chain Graphsstat.ML
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.
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 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.
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the t…
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.
Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching. First-order and higher-order Markov chains have been widely used methods to study such se…
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.
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.
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.
Algorithm learns mixtures of Markov chains and MDPs from short trajectories.
problem Learning mixtures of Markov chains and MDPs from short unlabeled trajectories.
method Subspace estimation, spectral clustering, EM algorithm, model estimation, classification.
result 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming EM algorithm with random initialization.
Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reductioncs.LG
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified…
The paper bounds generalization errors for deep neural networks with Markov datasets.
problem Bounding generalization errors for deep learning with Markov datasets.
method Developed new symmetrization inequalities for Markov chains, using spectral gap of the infinitesimal generator.
result Derived upper bounds on generalization errors for deep neural networks with Markov datasets.
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
New insights into Markov chain geometry via positive transition measures.
problem Lack of statistical meaning in the space of transition probabilities.
method Constructing an extension of the space of transition probabilities using Amari's theory of positive measures.
result Introduction of a new dually flat structure for the space of positive transition measures.
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
New method estimates convergence bounds for nonlinear Markov chains.
problem Difficulty in describing properties of nonlinear Markov chains.
method Coupling Markov chains to reconstitute distribution relationships and estimate convergence bounds.
result Estimation of convergence bounds is more precise than existing results.