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.
Previous research has also examined the use of continuous side information to complement sequential observation when learning latent features. Input-output HMMs @cite_21 and TRBMs @cite_11 consider the task of supervised learning where the observed variables influence both latent and output variables. However, these approaches assume that input observations for each time point are known. GCHMMs @cite_14 consider an HMM where transition probabilities are associated with side information. CRBMs @cite_23 incorporate side information into the factorization of weights in conditional RBMs. The RUPA method @cite_0 learns an HMM with additional responses via augmented visit aggregation. However, point estimate approximation over expected visits ignores the true distribution of visits. As a result, convergence problems may arise, especially when the distribution of visits has multiple modes. In contrast, our method uses Viterbi path integration to directly approximate the true posterior of visits. In summary, we consider the responses as both extra information for learning a latent representation of sequential observation, and a variable to predict. Considering the dual task simultaneously enforces interpretability, while maintaining predictive power.
@cite_14 @cite_21 @cite_0 @cite_23 @cite_11
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We have already shown that extracting long-term dependencies from sequential data is difficult, both for determimstic dynamical systems such as recurrent networks, and probabilistic models such as hidden Markov models (HMMs) or input output hidden Markov models (IOHMMs). In practice, to avoid this problem, researchers have used domain specific a-priori knowledge to give meaning to the hidden or state variables representing past context. In this paper, we propose to use a more general type of a-priori knowledge, namely that the temporal dependencies are structured hierarchically. This implies that long-term dependencies are represented by variables with a long time scale. This principle is applied to a recurrent network which includes delays and multiple time scales. Experiments confirm the advantages of such structures. A similar approach is proposed for HMMs and IOHMMs. Continual Learning in artificial neural networks suffers from interference and forgetting when different tasks are learned sequentially. This paper introduces the Active Long Term Memory Networks (A-LTM), a model of sequential multi-task deep learning that is able to maintain previously learned association between sensory input and behavioral output while acquiring knew knowledge. A-LTM exploits the non-convex nature of deep neural networks and actively maintains knowledge of previously learned, inactive tasks using a distillation loss. Distortions of the learned input-output map are penalized but hidden layers are free to transverse towards new local optima that are more favorable for the multi-task objective. We re-frame the McClelland's seminal Hippocampal theory with respect to Catastrophic Inference (CI) behavior exhibited by modern deep architectures trained with back-propagation and inhomogeneous sampling of latent factors across epochs. We present empirical results of non-trivial CI during continual learning in Deep Linear Networks trained on the same task, in Convolutional Neural Networks when the task shifts from predicting semantic to graphical factors and during domain adaptation from simple to complex environments. We present results of the A-LTM model's ability to maintain viewpoint recognition learned in the highly controlled iLab-20M dataset with 10 object categories and 88 camera viewpoints, while adapting to the unstructured domain of Imagenet with 1,000 object categories. In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric model where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the standard EM algorithm can be adapted to infer the model parameters. For the initialization step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the combining criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN. The statistical use of a particular classic form of a connectionist system, the multilayer perceptron (MLP), is described in the context of the recognition of continuous speech. A discriminant hidden Markov model (HMM) is defined, and it is shown how a particular MLP with contextual and extra feedback input units can be considered as a general form of such a Markov model. A link between these discriminant HMMs, trained along the Viterbi algorithm, and any other approach based on least mean square minimization of an error function (LMSE) is established. It is shown theoretically and experimentally that the outputs of the MLP (when trained along the LMSE or the entropy criterion) approximate the probability distribution over output classes conditioned on the input, i.e. the maximum a posteriori probabilities. Results of a series of speech recognition experiments are reported. The possibility of embedding MLP into HMM is described. Relations with other recurrent networks are also explained. >