New spectral method learns DNA methylation models efficiently.
problem Learning parameters of Binomial HMMs for DNA methylation data.
method Feature-map based approach exploiting Binomial HMM properties.
result The new algorithm provides theoretical guarantees and performs well on real data.
GMM-HMMs improve malware classification compared to discrete HMMs.
problem Improving malware classification accuracy using GMM-HMM models.
method Used GMM-HMM models for opcode and entropy-based features comparison with discrete HMMs.
result GMM-HMMs generally improve significantly on entropy-based features classification results.
Develops a more flexible HDP-HMM for temporal data segmentation.
problem Limited expressiveness of sticky HDP-HMM due to stationary self-persistence probability.
method Introduces recurrent sticky HDP-HMM with a novel Gibbs sampling strategy.
result RS-HDP-HMM outperforms other models in segmentation tasks.
A new model separates persistence and transition priors in HDP-HMM.
problem Limitation of sticky HDP-HMM in expressing different persistence strengths.
method Developed a disentangled sticky HDP-HMM (DS-HDP-HMM) with novel Gibbs sampling algorithms.
result DS-HDP-HMM outperforms sticky HDP-HMM and HDP-HMM on synthetic and real data.
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We focus on recurrent neural networks (RNNs), state of the art models in speech re…
Hybridizes LSTM and HMM for improved language model performance.
problem Improving the performance of LSTM and HMM models.
method Analyzes hidden state structures, compares predictive accuracy and hidden state output of LSTM and HMM.
result HMM can serve as an appropriate approximation of LSTM model.
HMRNN combines HMMs and neural networks for Alzheimer's disease forecasting.
problem Improving disease progression modeling with hidden states not fully known.
method Developed HMRNN combining HMMs and recurrent neural networks.
result HMRNN improves disease forecasting and offers novel clinical interpretation.
New binomial model fits all moments to geometric Brownian motion.
problem Discontinuity problem in option pricing.
method Constructs a generalized binomial tree model.
result Resolves discontinuity problem in option pricing.
Study on learning overcomplete Hidden Markov Models (HMMs).
problem Learning overcomplete HMMs with small output alphabets and sparse transition matrices.
method Analyzed both positive and negative results for efficient learning of overcomplete HMMs.
result Positive results for HMMs with sparse, well-conditioned, and short-cycled transition matrices.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
The paper uses HMM and LSTM for stock market trend analysis.
problem Predicting stock market trends using machine learning.
method Apply Hidden Markov Model and Long Short Term Memory to stock market data.
result The combination of GMM-HMM+LSTM and XGB-HMM+LSTM outperformed other models.
LC-CRFs are equivalent to HMMs, and MPM/MAP classifiers can be reformulated as CRFs.
problem Comparing and reformulating HMMs and CRFs.
method Demonstrating equivalence and reformulation of classifiers.
result LC-CRFs are equivalent to HMMs, and MPM/MAP classifiers can be reformulated as CRFs.
Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
The hidden Markov model (HMM) is a generative model that treats sequential data under the assumption that each observation is conditioned on the state of a discrete hidden variable that evolves in time as a Markov chain. In this paper, we derive a novel algorithm to cluster HMMs through their probability distributions.…
Combines LSTM with HMM to improve interpretability of RNNs.
problem Making deep neural networks more understandable and interpretable.
method Integrates LSTM and HMM, training them sequentially or jointly.
result A hybrid model outperforms standalone LSTM, especially on smaller datasets.
Optimized HMM using PSO overcomes constraints for better solutions.
problem Finding global optimal solutions for HMM parameters.
method Constrained Particle Swarm Optimization (PSO) to solve HMM parameters, re-normalization and re-mapping to enforce constraints.
result PSOHMM finds better solutions and converges faster than BWHMM.
New method estimates HMM hidden states efficiently.
problem Inaccurate posterior predictive distribution in HMMs.
method Autoregressive-flow for estimating hidden states.
result Estimates comparable to SMC algorithm.
HMMs improve music transcription accuracy.
problem Improving automatic transcription of music.
method Employed PLCA for multi-pitch estimation and integrated HMMs for note segmentation and post-processing.
result HMMs enhance transcription accuracy on different instruments.
Paper tackles HMM learning with unknown missing observation locations.
problem Learning HMMs with missing data locations unknown.
method Proposes reconstruction algorithms without structural assumptions.
result Can reconstruct process dynamics as if missing locations were known.
A new metric for comparing HMMs, especially GMM-HMMs, without Monte Carlo samples.
problem Comparing Hidden Markov Models (HMMs) with Gaussian conditional distributions.
method Aggregated Wasserstein metric based on optimal transport between Gaussian mixtures.
result The Aggregated Wasserstein metric is a semi-metric that can be computed efficiently and is invariant to state relabeling.
Cloned HMMs efficiently learn variable order sequences without local minima issues.
problem Learning long-term temporal structure in sequences.
method Constrained HMMs with a sparsity structure that maps hidden states deterministically to emissions.
result Cloned HMMs can model temporal dependencies at arbitrarily long distances and recognize contexts with 'holes'.
Paper tackles efficient HMM learning with conditional samples.
problem Cryptographic hardness in learning HMMs from i.i.d. samples.
method Interactive access model, polynomial-time algorithms for conditional probabilities and latent low rank structures.
result Efficient algorithms for HMM learning in both exact and approximate conditional settings.
Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the distributions of the sources. A standard approach to this problem is to model the …
The hidden Markov model (HMM) is a widely-used generative model that copes with sequential data, assuming that each observation is conditioned on the state of a hidden Markov chain. In this paper, we derive a novel algorithm to cluster HMMs based on the hierarchical EM (HEM) algorithm. The proposed algorithm i) cluster…
Extends CRR model with q-binomial random walks for asset pricing.
problem Asset pricing with time-varying probabilities and trend parameters.
method Introduces a q-binomial extension of the CRR model with non-self-similar binomial trees.
result Convergence to Black-Scholes formula with rate O(N^(-1/2)).
Analysis of pretrained models' effectiveness in downstream tasks.
problem Understanding why pretrained models perform well in NLP tasks.
method Analyzed head and prompt tuning approaches using latent variable models.
result Prompt tuning provides stronger guarantees than head tuning.
New nonparametric HMM improves genetic sequence analysis.
problem Improving genetic sequence data analysis for hidden states and transitions.
method Developed a nonparametric hierarchical Dirichlet process HMM for genetic sequence data.
result Our model provides more parsimonious parameterization of genetic processes.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture model…
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double sided HMM. This makes it possible to use ergodic theorems. As an applicatio…
Breaks circular dependency in synthetic option pricing with a novel model.
problem Circular dependency in implied volatility limits synthetic data for machine learning and risk analysis.
method Uses a Jump-Hidden Markov Model to generate price paths and a modified Heston process to convert paths into implied volatility.
result Framework generates realistic synthetic American option prices without external calibration.
Paper develops efficient method for probability estimation.
problem Estimating probabilities with high efficiency.
method Adaptive Monte Carlo estimation using truncated inverse binomial sampling.
result Proposed method is orders of magnitude more efficient.
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insur…
New method detects anomalies in time series data using HMMs.
problem Detect anomalies in discrete time series data.
method HMM gauge likelihood analysis (HMM GLA) using Baum-Welch algorithm and clustering.
result Successfully detects anomalies in synthetic and real-world syslog data.
Two methods use DNN-HMM for global SNR estimation of speech signals.
problem Estimating global SNR of speech signals in various noise conditions.
method Dropout approximation for uncertainty estimation and noise-specific regressors.
result Improved SNR estimation accuracy compared to existing methods.
Efficiently models tree-like data with coupled branches using HMMs.
problem Modeling sequential data with coupled branches in biological systems.
method Developed a dynamic programming algorithm for tree-based HMMs with coupled branches.
result Efficiently solves likelihood, decoding, and parameter learning problems for tree-based HMMs with coupled branches.
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
Enhances binomial and trinomial models for equity options pricing.
problem Improving accuracy of equity option pricing models.
method Develops time-dependent binomial model and introduces a risk-neutral trinomial tree.
result Equates moments of pricing tree increments to geometric Brownian motion.
Enhances fraud detection with multiple HMM perspectives.
problem Detecting credit card fraud from sequential transactions.
method Modeling credit card transactions from three perspectives (card-holder, terminal, amount/time) using HMMs and combining likelihoods as features.
result 15% increase in precision-recall AUC compared to state-of-the-art methods.
Correction for Error estimates for binomial approximations of game options [math.PR/0607123]
Improved binomial model for American put prices with error analysis.
problem Improving the accuracy of American put price approximations.
method Binomial approximation in the Black-Scholes model with consideration of continuous dividend yield.
result Error in approximation is O((lnn)α/n), where α depends on interest rate and dividend yield. Scalable hybrid HMM with Gaussian Process for time-series data clustering.
problem Large number of parameters and long sequences in time-series data make HMM-GPSM training difficult.
method Stochastic Variational Inference (SVI) for long sequences and reparameterized random Fourier features (R-RFF) for large data points.
result Significant reduction in training time and improved hidden-state estimation accuracy.
Develops a binomial model in categorical probability spaces.
problem Valuation of financial claims in non-standard filtrations.
method Introduces generalized filtrations in a categorical setting.
result Validates financial claim valuations in new filtrations.
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an …
The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…
Bayesian HMM for protein alignment state estimation.
problem Estimating the MAP state sequence for a Bayesian HMM.
method Training data with Dirichlet priors, iterative algorithms for MAP path estimation.
result Bayesian setup outperforms frequentist estimation in protein alignment.
Study investigates estimation error in EMHMM simulations.
problem Estimation error in Hidden Markov Models (HMMs) with EMHMM.
method Simulation study using variational Bayesian inference.
result KL divergence and L1-norm relate to estimation error and ground-truth HMM parameters.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.