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Acoustic models using probabilistic linear discriminant analysis (PLDA) capture the correlations within feature vectors using subspaces which do not vastly expand the model. This allows high dimensional and correlated feature spaces to be used, without requiring the estimation of multiple high dimension covariance matrices. In this letter we extend the recently presented PLDA mixture model for speech recognition through a tied PLDA approach, which is better able to control the model size to avoid overfitting. We carried out experiments uisng the Switchboard corpus, with both mel frequency cepstral coefficient features and bottleneck feature derived from a deep neural network. Reductions in word error rate were obtained by using tied PLDA, compared with the PLDA mixture model, subspace Gaussian mixture models, and deep neural networks.
Tied Probabilistic Linear Discriminant Analysis for Speech Recognition

Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on optimism in the face of uncertainty or intrinsic motivation. In this work, we describe a surprising finding: a simple generalization of the classic count-based approach can reach near state-of-the-art performance on various highdimensional and/or continuous deep RL benchmarks. States are mapped to hash codes, which allows to count their occurrences with a hash table. These counts are then used to compute a reward bonus according to the classic count-based exploration theory. We find that simple hash functions can achieve surprisingly good results on many challenging tasks. Furthermore, we show that a domain-dependent learned hash code may further improve these results. Detailed analysis reveals important aspects of a good hash function: 1) having appropriate granularity and 2) encoding information relevant to solving the MDP. This exploration strategy achieves near state-of-the-art performance on both continuous control tasks and Atari 2600 games, hence providing a simple yet powerful baseline for solving MDPs that require considerable exploration.
#Exploration:A Study of Count-Based Explorationfor Deep Reinforcement Learning

<lb>The minimization of the logistic loss is a popular approach to batch supervised learning. Our<lb>paper starts from the surprising observation that, when fitting linear (or kernelized) classifiers,<lb>the minimization of the logistic loss is equivalent to the minimization of an exponential rado-loss<lb>computed (i) over transformed data that we call Rademacher observations (rados), and (ii) over<lb>the same classifier as the one of the logistic loss. Thus, a classifier learnt from rados can be<lb>directly used to classify observations. We provide a learning algorithm over rados with boosting-<lb>compliant convergence rates on the logistic loss (computed over examples). Experiments on<lb>domains with up to millions of examples, backed up by theoretical arguments, display that<lb>learning over a small set of random rados can challenge the state of the art that learns over<lb>the complete set of examples. We show that rados comply with various privacy requirements<lb>that make them good candidates for machine learning in a privacy framework. We give several<lb>algebraic, geometric and computational hardness results on reconstructing examples from rados.<lb>We also show how it is possible to craft, and efficiently learn from, rados in a differential privacy<lb>framework. Tests reveal that learning from differentially private rados can compete with learning<lb>from random rados, and hence with batch learning from examples, achieving non-trivial privacy<lb>vs accuracy tradeoffs.

Rademacher Observations, Private Data, and Boosting