Sorry if this is too trivial, but let me start at the "very beginning:" Linear regression. The goal of (ordinary least-squares) linear regression is to find the optimal weights that -- when linearly combined with the inputs -- result in a model that minimizes the vertical offsets between the target and explanatory variables, but let's not get distracted by model fitting, which is a different topic;). So, in linear regression, we compute a linear combination of weights and inputs (let's call this function the "net input function"). Next, let's consider logistic regression. Here, we put the net input z through a non-linear "activation function" -- the logistic sigmoid function where.

In Machine Learning (ML), we typically care about optimizing for a particular metric, whether this is a score on a certain benchmark or a business KPI. In order to do this, we generally train a single model or an ensemble of models to perform our desired task. While we can generally achieve acceptable performance this way, by being laser-focused on our single task, we ignore information that might help us do even better on the metric we care about. Specifically, this information comes from the training signals of related tasks. By sharing representations between related tasks, we can enable our model to generalize better on our original task. This approach is called Multi-Task Learning (MTL) and will be the topic of this blog post. Multi-task learning has been used successfully across all applications of machine learning, from natural language processing [1] and speech recognition [2] to computer vision [3] and drug discovery [4]. MTL comes in many guises: joint learning, learning to learn, and learning with auxiliary tasks are only some names that have been used to refer to it. Generally, as soon as you find yourself optimizing more than one loss function, you are effectively doing multi-task learning (in contrast to single-task learning). In those scenarios, it helps to think about what you are trying to do explicitly in terms of MTL and to draw insights from it.

From the above plot, it is evident that the clusters 1, 7, and 9 have activity for all 24 hours and are the more revenue generating clusters. The clusters 1, 5, 7, 9, and 10 have activity in night hours. The cluster 5 has activity from 11.5 to 17 hours. By using this clustering mechanism, you can find the clusters making more traffic to the telecom network in the measure of total activity. Similarly, you can obtain more information like square grid and country code information to understand the square grid likely creating more revenue and more traffic to the telecom network and to target high customers based on their geo location. In the upcoming blog, we will discuss about how RFM will be used to analyze call detail records. Bio: Rathnadevi Manivannan is working as a Senior Technical Writer in Treselle Systems, experienced and passionate about writing on different technologies and domains such as Big Data, Cloud Computing, Virtualization, Storage, Data Analytics, Business Analytics.

Here we discuss general applications of statistical models, whether they arise from data science, operations research, engineering, machine learning or statistics. We do not discuss specific algorithms such as decision trees, logistic regression, Bayesian modeling, Markov models, data reduction or feature selection. Instead, I discuss frameworks - each one using its own types of techniques and algorithms - to solve real life problems. Most of the entries below are found in Wikipedia, and I have used a few definitions or extracts from the relevant Wikipedia articles, in addition to personal contributions. Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively.

Written by Chris Fonnesbeck, Assistant Professor of Biostatistics, Vanderbilt University Medical Center. You can view, fork, and play with this project on the Domino data science platform. A common applied statistics task involves building regression models to characterize non-linear relationships between variables. It is possible to fit such models by assuming a particular non-linear functional form, such as a sinusoidal, exponential, or polynomial function, to describe one variable's response to the variation in another. Unless this relationship is obvious from the outset, however, it involves possibly extensive model selection procedures to ensure the most appropriate model is retained. Alternatively, a non-parametric approach can be adopted by defining a set of knots across the variable space and use a spline or kernel regression to describe arbitrary non-linear relationships.

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In this work, we design a machine learning based method, online adaptive primal support vector regression (SVR), to model the implied volatility surface. The algorithm proposed is the first derivation and implementation of an online primal kernel SVR. It features enhancements that allow online adaptive learning by embedding the idea of local fitness and budget maintenance. To accelerate our algorithm, we implement its most computationally intensive parts in a Field Programmable Gate Arrays hardware. Using intraday tick data from the E-mini S&P 500 options market, we show that our algorithm outperforms two competing methods and the Gaussian kernel is a better choice than the linear kernel. Sensitivity analysis is also presented to demonstrate how hyper parameters affect the error rates and the number of support vectors in our models.

Performance of machine learning approaches depends strongly on the choice of misfit penalty, and correct choice of penalty parameters, such as the threshold of the Huber function. These parameters are typically chosen using expert knowledge, cross-validation, or black-box optimization, which are time consuming for large-scale applications. We present a principled, data-driven approach to simultaneously learn the model pa- rameters and the misfit penalty parameters. We discuss theoretical properties of these joint inference problems, and develop algorithms for their solution. We show synthetic examples of automatic parameter tuning for piecewise linear-quadratic (PLQ) penalties, and use the approach to develop a self-tuning robust PCA formulation for background separation.

Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation. The learned embeddings could advance various learning tasks such as node classification, network clustering, and link prediction. Most, if not all, of the existing work, is overwhelmingly performed in the context of plain and static networks. Nonetheless, in reality, network structure often evolves over time with addition/deletion of links and nodes. Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content and the fading of old content. These changing characteristics motivate us to seek an effective embedding representation to capture network and attribute evolving patterns, which is of fundamental importance for learning in a dynamic environment. To our best knowledge, we are the first to tackle this problem with the following two challenges: (1) the inherently correlated network and node attributes could be noisy and incomplete, it necessitates a robust consensus representation to capture their individual properties and correlations; (2) the embedding learning needs to be performed in an online fashion to adapt to the changes accordingly. In this paper, we tackle this problem by proposing a novel dynamic attributed network embedding framework - DANE. In particular, DANE provides an offline method for a consensus embedding first and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner. We perform extensive experiments on both synthetic and real attributed networks to corroborate the effectiveness and efficiency of the proposed framework.

It is challenging to develop stochastic gradient based scalable inference for deep discrete latent variable models (LVMs), due to the difficulties in not only computing the gradients, but also adapting the step sizes to different latent factors and hidden layers. For the Poisson gamma belief network (PGBN), a recently proposed deep discrete LVM, we derive an alternative representation that is referred to as deep latent Dirichlet allocation (DLDA). Exploiting data augmentation and marginalization techniques, we derive a block-diagonal Fisher information matrix and its inverse for the simplex-constrained global model parameters of DLDA. Exploiting that Fisher information matrix with stochastic gradient MCMC, we present topic-layer-adaptive stochastic gradient Riemannian (TLASGR) MCMC that jointly learns simplex-constrained global parameters across all layers and topics, with topic and layer specific learning rates. State-of-the-art results are demonstrated on big data sets.