Welcome to the third article in a five-part series about machine learning. In this article, we'll continue our machine learning discussion, and focus on problems associated with overfitting data, as well as controlling model complexity, a model evaluation and errors introduction, model validation and tuning, and improving model performance. Overfitting is one of the greatest concerns in predictive analytics and machine learning. Overfitting refers to a situation where the model chosen to fit the training data fits too well, and essentially captures all of the noise, outliers, and so on. The consequence of this is that the model will fit the training data very well, but will not accurately predict cases not represented by the training data, and therefore will not generalize well to unseen data.

In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Using probabilistic matrix factorization techniques and acquisition functions from Bayesian optimization, we exploit experiments performed in hundreds of different datasets to guide the exploration of the space of possible pipelines. In our experiments, we show that our approach quickly identifies high-performing pipelines across a wide range of datasets, significantly outperforming the current state-of-the-art.

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, we propose a new completion algorithm based on the proposed norms. A key advantage of the proposed norms is that it is convex and can find a globally optimal solution, while existing methods for coupled learning are non-convex. Furthermore, we analyze the excess risk bounds of the completion model regularized by our proposed norms which show that our proposed norms can exploit the low rankness of coupled tensors leading to better bounds compared to uncoupled norms. Through synthetic and real-world data experiments, we show that the proposed completion algorithm compares favorably with existing completion algorithms.

Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be processed efficiently in terms of both time and space. Current semi-supervised graph embedding algorithms assume the labelled nodes are given, which may not be always true in the real world. While manually label all training data is inapplicable, how to select the subset of training data to label so as to maximize the graph analysis task performance is of great importance. This motivates our proposed active graph embedding (AGE) framework, in which we design a general active learning query strategy for any semi-supervised graph embedding algorithm. AGE selects the most informative nodes as the training labelled nodes based on the graphical information (i.e., node centrality) as well as the learnt node embedding (i.e., node classification uncertainty and node embedding representativeness). Different query criteria are combined with the time-sensitive parameters which shift the focus from graph based query criteria to embedding based criteria as the learning progresses. Experiments have been conducted on three public data sets and the results verified the effectiveness of each component of our query strategy and the power of combining them using time-sensitive parameters. Our code is available online at: https://github.com/vwz/AGE.

This work proposes a novel method for semi-supervised learning from partially labeled massive network-structured datasets, i.e., big data over networks. We model the underlying hypothesis, which relates data points to labels, as a graph signal, defined over some graph (network) structure intrinsic to the dataset. Following the key principle of supervised learning, i.e., "similar inputs yield similar outputs", we require the graph signals induced by labels to have small total variation. Accordingly, we formulate the problem of learning the labels of data points as a non-smooth convex optimization problem which amounts to balancing between the empirical loss, i.e., the discrepancy with some partially available label information, and the smoothness quantified by the total variation of the learned graph signal. We solve this optimization problem by appealing to a recently proposed preconditioned variant of the popular primal-dual method by Pock and Chambolle, which results in a sparse label propagation algorithm. This learning algorithm allows for a highly scalable implementation as message passing over the underlying data graph. By applying concepts of compressed sensing to the learning problem, we are also able to provide a transparent sufficient condition on the underlying network structure such that accurate learning of the labels is possible. We also present an implementation of the message passing formulation allows for a highly scalable implementation in big data frameworks.

Recently, I began a series on exploratory data analysis; so far, I have written about computing descriptive statistics and creating box plots in R for a univariate data set with missing values. Today, I will continue this series by analyzing the same data set with kernel density estimation, a useful non-parametric technique for visualizing the underlying distribution of a continuous variable.

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.

Thank you very much, as for your question, I meant that I have an univariate logistic regression model (i.e., with only one dependent binary variable), where the dependent variable must be explained by a number of binary independent variables (1,0). I have no problem when the independent variables are continuous in nature and normally distributed, because there is Hsieh (1998) who said that you can obtain the total sample size basing on the multiple correlation coefficient between Xi and the remaining predictors... However I didn't find anything like that for the model that I talked about above. So I hope to find in APPLIED LOGISTIC REGRESSION what I looking for.

Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster convergence of restarting APG method relies on the potentially unknown constant in QGC to appropriately restart APG, which restricts its applicability. We address this issue by developing a novel adaptive gradient converging methods, i.e., leveraging the magnitude of proximal gradient as a criterion for restart and termination. Our analysis extends to a much more general condition beyond the QGC, namely the H\"{o}lderian error bound (HEB) condition. {\it The key technique} for our development is a novel synthesis of {\it adaptive regularization and a conditional restarting scheme}, which extends previous work focusing on strongly convex problems to a much broader family of problems. Furthermore, we demonstrate that our results have important implication and applications in machine learning: (i) if the objective function is coercive and semi-algebraic, PG's convergence speed is essentially $o(\frac{1}{t})$, where $t$ is the total number of iterations; (ii) if the objective function consists of an $\ell_1$, $\ell_\infty$, $\ell_{1,\infty}$, or huber norm regularization and a convex smooth piecewise quadratic loss (e.g., squares loss, squared hinge loss and huber loss), the proposed algorithm is parameter-free and enjoys a {\it faster linear convergence} than PG without any other assumptions (e.g., restricted eigen-value condition). It is notable that our linear convergence results for the aforementioned problems are global instead of local. To the best of our knowledge, these improved results are the first shown in this work.

Two-Class Support Vector Machine is used to create a model that is based on the Support Vector Machine Algorithm.The classifier that this module initializes is useful for predicting between two possible outcomes that depend on continuous or categorical predictor variables. This model is a supervised learning method and therefore, requires a dataset which includes a labeled column. You can train the model by providing the model and the tagged dataset as an input to Train Model or Tune Model Hyperparameters. The trained model can then be used to predict values for the new input examples. Support Vector Machines (SVMs) are supervised learning models that analyze data and recognize patterns.