A linear memory algorithm for Baum-Welch training

Background: Baum-Welch training is an expectation-maximisation algorithm for training the emission and transition probabilities of hidden Markov models in a fully automated way. Methods and results: We introduce a linear space algorithm for Baum-Welch training. For a hidden Markov model with M states, T free transition and E free emission parameters, and an input sequence of length L, our new algorithm requires O(M) memory and O(L M T_max (T + E)) time for one Baum-Welch iteration, where T_max is the maximum number of states that any state is connected to. The most memory efficient algorithm until now was the checkpointing algorithm with O(log(L) M) memory and O(log(L) L M T_max) time requirement. Our novel algorithm thus renders the memory requirement completely independent of the length of the training sequences. More generally, for an n-hidden Markov model and n input sequences of length L, the memory requirement of O(log(L) L^(n-1) M) is reduced to O(L^(n-1) M) memory while the running time is changed from O(log(L) L^n M T_max + L^n (T + E)) to O(L^n M T_max (T + E)). Conclusions: For the large class of hidden Markov models used for example in gene prediction, whose number of states does not scale with the length of the input sequence, our novel algorithm can thus be both faster and more memory-efficient than any of the existing algorithms.Comment: 14 pages, 1 figure version 2: fixed some errors, final version of pape

Implementing EM and Viterbi algorithms for Hidden Markov Model in linear memory

<p>Abstract</p> <p>Background</p> <p>The Baum-Welch learning procedure for Hidden Markov Models (HMMs) provides a powerful tool for tailoring HMM topologies to data for use in knowledge discovery and clustering. A linear memory procedure recently proposed by <it>Miklós, I. and Meyer, I.M. </it>describes a memory sparse version of the Baum-Welch algorithm with modifications to the original probabilistic table topologies to make memory use independent of sequence length (and linearly dependent on state number). The original description of the technique has some errors that we amend. We then compare the corrected implementation on a variety of data sets with conventional and checkpointing implementations.</p> <p>Results</p> <p>We provide a correct recurrence relation for the emission parameter estimate and extend it to parameter estimates of the Normal distribution. To accelerate estimation of the prior state probabilities, and decrease memory use, we reverse the originally proposed forward sweep. We describe different scaling strategies necessary in all real implementations of the algorithm to prevent underflow. In this paper we also describe our approach to a linear memory implementation of the Viterbi decoding algorithm (with linearity in the sequence length, while memory use is approximately independent of state number). We demonstrate the use of the linear memory implementation on an extended Duration Hidden Markov Model (DHMM) and on an HMM with a spike detection topology. Comparing the various implementations of the Baum-Welch procedure we find that the checkpointing algorithm produces the best overall tradeoff between memory use and speed. In cases where sequence length is very large (for Baum-Welch), or state number is very large (for Viterbi), the linear memory methods outlined may offer some utility.</p> <p>Conclusion</p> <p>Our performance-optimized Java implementations of Baum-Welch algorithm are available at <url>http://logos.cs.uno.edu/~achurban</url>. The described method and implementations will aid sequence alignment, gene structure prediction, HMM profile training, nanopore ionic flow blockades analysis and many other domains that require efficient HMM training with EM.</p

Unsupervised Neural Hidden Markov Models

In this work, we present the first results for neuralizing an Unsupervised Hidden Markov Model. We evaluate our approach on tag in- duction. Our approach outperforms existing generative models and is competitive with the state-of-the-art though with a simpler model easily extended to include additional context.Comment: accepted at EMNLP 2016, Workshop on Structured Prediction for NLP. Oral presentatio

Duration modeling with expanded HMM applied to speech recognition

The occupancy of the HMM states is modeled by means of a Markov chain. A linear estimator is introduced to compute the probabilities of the Markov chain. The distribution function (DF) represents accurately the observed data. Representing the DF as a Markov chain allows the use of standard HMM recognizers. The increase of complexity is negligible in training and strongly limited during recognition. Experiments performed on acoustic-phonetic decoding shows how the phone recognition rate increases from 60.6 to 61.1. Furthermore, on a task of database inquires, where phones are used as subword units, the correct word rate increases from 88.2 to 88.4.Peer ReviewedPostprint (published version

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

ApHMM: Accelerating Profile Hidden Markov Models for Fast and Energy-Efficient Genome Analysis

Profile hidden Markov models (pHMMs) are widely employed in various bioinformatics applications to identify similarities between biological sequences, such as DNA or protein sequences. In pHMMs, sequences are represented as graph structures. These probabilities are subsequently used to compute the similarity score between a sequence and a pHMM graph. The Baum-Welch algorithm, a prevalent and highly accurate method, utilizes these probabilities to optimize and compute similarity scores. However, the Baum-Welch algorithm is computationally intensive, and existing solutions offer either software-only or hardware-only approaches with fixed pHMM designs. We identify an urgent need for a flexible, high-performance, and energy-efficient HW/SW co-design to address the major inefficiencies in the Baum-Welch algorithm for pHMMs. We introduce ApHMM, the first flexible acceleration framework designed to significantly reduce both computational and energy overheads associated with the Baum-Welch algorithm for pHMMs. ApHMM tackles the major inefficiencies in the Baum-Welch algorithm by 1) designing flexible hardware to accommodate various pHMM designs, 2) exploiting predictable data dependency patterns through on-chip memory with memoization techniques, 3) rapidly filtering out negligible computations using a hardware-based filter, and 4) minimizing redundant computations. ApHMM achieves substantial speedups of 15.55x - 260.03x, 1.83x - 5.34x, and 27.97x when compared to CPU, GPU, and FPGA implementations of the Baum-Welch algorithm, respectively. ApHMM outperforms state-of-the-art CPU implementations in three key bioinformatics applications: 1) error correction, 2) protein family search, and 3) multiple sequence alignment, by 1.29x - 59.94x, 1.03x - 1.75x, and 1.03x - 1.95x, respectively, while improving their energy efficiency by 64.24x - 115.46x, 1.75x, 1.96x.Comment: Accepted to ACM TAC

Learning a Hybrid Architecture for Sequence Regression and Annotation

When learning a hidden Markov model (HMM), sequen- tial observations can often be complemented by real-valued summary response variables generated from the path of hid- den states. Such settings arise in numerous domains, includ- ing many applications in biology, like motif discovery and genome annotation. In this paper, we present a flexible frame- work for jointly modeling both latent sequence features and the functional mapping that relates the summary response variables to the hidden state sequence. The algorithm is com- patible with a rich set of mapping functions. Results show that the availability of additional continuous response vari- ables can simultaneously improve the annotation of the se- quential observations and yield good prediction performance in both synthetic data and real-world datasets.Comment: AAAI 201

Diffusion of Context and Credit Information in Markovian Models

This paper studies the problem of ergodicity of transition probability matrices in Markovian models, such as hidden Markov models (HMMs), and how it makes very difficult the task of learning to represent long-term context for sequential data. This phenomenon hurts the forward propagation of long-term context information, as well as learning a hidden state representation to represent long-term context, which depends on propagating credit information backwards in time. Using results from Markov chain theory, we show that this problem of diffusion of context and credit is reduced when the transition probabilities approach 0 or 1, i.e., the transition probability matrices are sparse and the model essentially deterministic. The results found in this paper apply to learning approaches based on continuous optimization, such as gradient descent and the Baum-Welch algorithm.Comment: See http://www.jair.org/ for any accompanying file

HMMConverter 1.0: a toolbox for hidden Markov models

Hidden Markov models (HMMs) and their variants are widely used in Bioinformatics applications that analyze and compare biological sequences. Designing a novel application requires the insight of a human expert to define the model's architecture. The implementation of prediction algorithms and algorithms to train the model's parameters, however, can be a time-consuming and error-prone task. We here present HMMConverter, a software package for setting up probabilistic HMMs, pair-HMMs as well as generalized HMMs and pair-HMMs. The user defines the model itself and the algorithms to be used via an XML file which is then directly translated into efficient C++ code. The software package provides linear-memory prediction algorithms, such as the Hirschberg algorithm, banding and the integration of prior probabilities and is the first to present computationally efficient linear-memory algorithms for automatic parameter training. Users of HMMConverter can thus set up complex applications with a minimum of effort and also perform parameter training and data analyses for large data sets