Linear Regression is about fitting a straight line from the scatter plot,key challenge here what constitutes a best fit line in other words what would be best values of and . The general idea is to find a line ( its coefficients) such that total error is at the minimum. There is a standard explanation that we need to minimize the total square error, which means we have to solve a minimization problem to solve optimal values of the coefficients. Obviously this method involves quite a lot of mathematics or calculus etc. which would not provide any institution or illustration, instead we will use a little of vector algebra and associated geometry to build the intuition about the solution.

Thus, given a sequence of frames corresponding to an utterance, the model is required to produce, for each frame, a probability distribution over the alphabet. During the training phase, the softmax outputs are fed into a CTC cost function (more on this shortly) which uses the actual transcripts to (i) score the model's predictions, and (ii) generate an error signal quantifying the accuracy of the model's predictions. The overall goal is to train the model to increase the overall score of its predictions relative to the actual transcripts. Empirically, we have found that using stochastic gradient descent with momentum paired with gradient clipping leads to the best performing models. Deeper networks (seven layers or more) also tend to perform better in general.

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In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed model on the uncontaminated data that remains. To solve the resulting nonconvex optimization problem, we introduce a fast stochastic proximal-gradient algorithm that incorporates prior knowledge through nonsmooth regularization. For datasets of size $n$, our approach requires $O(n^{2/3}/\varepsilon)$ gradient evaluations to reach $\varepsilon$-accuracy and, when a certain error bound holds, the complexity improves to $O(\kappa n^{2/3}\log(1/\varepsilon))$. These rates are $n^{1/3}$ times better than those achieved by typical, full gradient methods.

Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally efficient classifier called high-dimensional RDA (HDRDA), designed for the small-sample, high-dimensional setting. For HDRDA, we show that each training observation, regardless of class, contributes to the class covariance matrix, resulting in an interpretable estimator that borrows from the pooled sample covariance matrix. Moreover, we show that HDRDA is equivalent to a classifier in a reduced-feature space with dimension approximately equal to the training sample size. As a result, the matrix operations employed by HDRDA are computationally linear in the number of features, making the classifier well-suited for high-dimensional classification in practice. We demonstrate that HDRDA is often superior to several sparse and regularized classifiers in terms of classification accuracy with three artificial and six real high-dimensional data sets. Also, timing comparisons between our HDRDA implementation in the sparsediscrim R package and the standard RDA formulation in the klaR R package demonstrate that as the number of features increases, the computational runtime of HDRDA is drastically smaller than that of RDA.

Consumer Demand Response (DR) is an important research and industry problem, which seeks to categorize, predict and modify consumer's energy consumption. Unfortunately, traditional clustering methods have resulted in many hundreds of clusters, with a given consumer often associated with several clusters, making it difficult to classify consumers into stable representative groups and to predict individual energy consumption patterns. In this paper, we present a shape-based approach that better classifies and predicts consumer energy consumption behavior at the household level. The method is based on Dynamic Time Warping. DTW seeks an optimal alignment between energy consumption patterns reflecting the effect of hidden patterns of regular consumer behavior. Using real consumer 24-hour load curves from Opower Corporation, our method results in a 50% reduction in the number of representative groups and an improvement in prediction accuracy measured under DTW distance. We extend the approach to estimate which electrical devices will be used and in which hours.

This paper maps the large-scale variation of the Spanish language by employing a corpus based on geographically tagged Twitter messages. Lexical dialects are extracted from an analysis of variants of tens of concepts. The resulting maps show linguistic variation on an unprecedented scale across the globe. We discuss the properties of the main dialects within a machine learning approach and find that varieties spoken in urban areas have an international character in contrast to country areas where dialects show a more regional uniformity.

The output of the face detector is scaled to 90x90 and fed directly to the facial expression analysis system (see Figure 1). The system is essentially the same as the one used for Automatic FACS coding. First the face image is passed through a bank of Gabor filters at 8 orientations and 9 scales (2-32 pixels/cycle at 0.5 octave steps). The filterbank representations are then channeled to a classifier to code the image in terms of a set of expression dimensions. We have found support vector machines to be very effective for classifying facial expressions (Littlewort et al., in press, Bartlett et al., 2003).

Domain adaptation deals with adapting classifiers trained on data from a source distribution, to work effectively on data from a target distribution. In this paper, we introduce the Nonlinear Embedding Transform (NET) for unsupervised domain adaptation. The NET reduces cross-domain disparity through nonlinear domain alignment. It also embeds the domain-aligned data such that similar data points are clustered together. This results in enhanced classification. To determine the parameters in the NET model (and in other unsupervised domain adaptation models), we introduce a validation procedure by sampling source data points that are similar in distribution to the target data. We test the NET and the validation procedure using popular image datasets and compare the classification results across competitive procedures for unsupervised domain adaptation.

One of the key information pieces in improving energy efficiency of buildings is the appliance level breakdown of energy consumption. Energy disaggregation is the process of obtaining this breakdown from a building level aggregate data using computational techniques. Most of the current research focuses on residential buildings, obtaining this information from a single smart meter and often relying on high frequency data. This work is directed at commercial buildings equipped with building management and automation systems providing low frequency operational and contextual data. This paper presents a machine learning method to disaggregate energy consumption of the building using this operational data as input features. Experimental results on two publicly available datasets demonstrate the effectiveness of the approach, which surpasses existing methods. For all but one appliance of House 2 of the publicly available REDD dataset, improvements in normalized error in assigned power range between 20% (Lighting) and 220% (Stove). For another dataset from an educational facility in Singapore, disaggregation accuracy of 92% is reported for the facility's cooling system.