**Probabilistic Kernel Support Vector Machine**

We propose a probabilistic enhancement of standard Kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available on each datum. In the present paper, we specifically consider Gaussian distributions to model uncertainty. Thereby, our data consist of pairs $(x_i,\Sigma_i)$, $i\in ,…,N$, along with an indicator $y_i\in(-1,1)$ to declare membership in one of two categories for each pair. These pairs may be viewed to represent the mean and covariance, respectively, of random vectors $\xi_i$ taking values in a suitable linear space (typically ${\mathbb R}^n$). Thus, our setting may also be viewed as a modification of Support Vector Machines to classify distributions, albeit, at present, only Gaussian ones. We outline the formalism that allows computing suitable classifiers via a natural modification of the standard ‘kernel trick’. The main contribution of this work is to point out a suitable kernel function for applying Support Vector techniques to the setting of uncertain data for which a detailed uncertainty description is also available (herein, ‘Gaussian points’). … **Principal Model Analysis (PMA)**

Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In the method, multiple PLS models are trained on sub-training sets, derived from the original training set based on the random sampling with replacement method. The regression coefficients of all the sub-PLS models are fused in a joint regression coefficient matrix. The final projection direction is then estimated by performing the PCA on the joint regression coefficient matrix. The proposed PMA method is compared with other traditional dimension reduction methods, such as PLS, Bagging PLS, Linear discriminant analysis (LDA) and PLS-LDA. Experimental results on six public datasets show that our proposed method can achieve better classification performance and is usually more stable. … **Layer Trajectory LSTM (ltLSTM)**

It is popular to stack LSTM layers to get better modeling power, especially when large amount of training data is available. However, an LSTM-RNN with too many vanilla LSTM layers is very hard to train and there still exists the gradient vanishing issue if the network goes too deep. This issue can be partially solved by adding skip connections between layers, such as residual LSTM. In this paper, we propose a layer trajectory LSTM (ltLSTM) which builds a layer-LSTM using all the layer outputs from a standard multi-layer time-LSTM. This layer-LSTM scans the outputs from time-LSTMs, and uses the summarized layer trajectory information for final senone classification. The forward-propagation of time-LSTM and layer-LSTM can be handled in two separate threads in parallel so that the network computation time is the same as the standard time-LSTM. With a layer-LSTM running through layers, a gated path is provided from the output layer to the bottom layer, alleviating the gradient vanishing issue. Trained with 30 thousand hours of EN-US Microsoft internal data, the proposed ltLSTM performed significantly better than the standard multi-layer LSTM and residual LSTM, with up to 9.0% relative word error rate reduction across different tasks. … **Teaching Explanations for Decisions (TED)**

Artificial intelligence systems are being increasingly deployed due to their potential to increase the efficiency, scale, consistency, fairness, and accuracy of decisions. However, as many of these systems are opaque in their operation, there is a growing demand for such systems to provide explanations for their decisions. Conventional approaches to this problem attempt to expose or discover the inner workings of a machine learning model with the hope that the resulting explanations will be meaningful to the consumer. In contrast, this paper suggests a new approach to this problem. It introduces a simple, practical framework, called Teaching Explanations for Decisions (TED), that provides meaningful explanations that match the mental model of the consumer. We illustrate the generality and effectiveness of this approach with two different examples, resulting in highly accurate explanations with no loss of prediction accuracy for these two examples. …

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