Short note on two output-dependent hidden Markov models

The purpose of this note is to study the assumption of mutual information independence", which is used by Zhou (2005) for deriving an output-dependent hidden Markov model, the so-called discriminative HMM (D-HMM), in the context of determining a stochastic optimal sequence of hidden states. The assumption is extended to derive its generative counterpart, the G-HMM. In addition, state-dependent representations for two output-dependent HMMs, namely HMMSDO (Li, 2005) and D-HMM, are presented

Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin

Housing Market Crash Prediction Using Machine Learning and Historical Data

The 2008 housing crisis was caused by faulty banking policies and the use of credit derivatives of mortgages for investment purposes. In this project, we look into datasets that are the markers to a typical housing crisis. Using those data sets we build three machine learning techniques which are, Linear regression, Hidden Markov Model, and Long Short-Term Memory. After building the model we did a comparative study to show the prediction done by each model. The linear regression model did not predict a housing crisis, instead, it showed that house prices would be rising steadily and the R-squared score of the model is 0.76. The Hidden Markov Model predicted a fall in the house prices and the R-squared score for this model is 0.706. Lastly, the Long Short-Term Memory showed that the house price would fall briefly but would stabilize after that. Also, fall is not as sharp as what was predicted by the HMM model. The R- squared scored for this model is 0.9, which is the highest among all other models. Although the R-squared score doesn’t say how accurate a model it definitely says how closely a model fits the data. From our model R-square score the model that best fits the data was LSTM. As the dataset used in all the models are the same therefore it is safe to say the prediction made by LSTM is better than the other ones

Learning Hybrid System Models for Supervisory Decoding of Discrete State, with applications to the Parietal Reach Region

Based on Gibbs sampling, a novel method to identify mathematical models of neural activity in response to temporal changes of behavioral or cognitive state is presented. This work is motivated by the developing field of neural prosthetics, where a supervisory controller is required to classify activity of a brain region into suitable discrete modes. Here, neural activity in each discrete mode is modeled with nonstationary point processes, and transitions between modes are modeled as hidden Markov models. The effectiveness of this framework is first demonstrated on a simulated example. The identification algorithm is then applied to extracellular neural activity recorded from multi-electrode arrays in the parietal reach region of a rhesus monkey, and the results demonstrate the ability to decode discrete changes even from small data sets