We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These heuristics can be used to find good, if not global, solutions and appear to work well in practice. We also describe an alternative formulation, based on the perspective transformation, which makes the problem amenable to mixed-integer convex programming and yields computationally tractable lower bounds. We illustrate one of our heuristic methods by applying it to various examples and use the perspective transformation to certify that the solutions are relatively close to the global optimum. This paper is accompanied by an open-source implementation.

Variable selection is of significant importance for classification and regression tasks in machine learning and statistical applications where both predictability and explainability are needed. In this paper, a Copula Entropy (CE) based method for variable selection which use CE based ranks to select variables is proposed. The method is both model-free and tuning-free. Comparison experiments between the proposed method and traditional variable selection methods, such as Stepwise Selection, regularized generalized linear models and Adaptive LASSO, were conducted on the UCI heart disease data. Experimental results show that CE based method can select the `right' variables out effectively and derive better interpretable results than traditional methods do without sacrificing accuracy performance. It is believed that CE based variable selection can help to build more explainable models.

Data Science for Marketing Analytics: Achieve your marketing goals with the data analytics power of Python Explore new and more sophisticated tools that reduce your marketing analytics efforts and give you precise results Key Features Study new techniques for marketing analytics Explore uses of machine learning to power your marketing analyses Work through each stage of data analytics with the help of multiple examples and exercises Book Description Data Science for Marketing Analytics covers every stage of data analytics, from working with a raw dataset to segmenting a population and modeling different parts of the population based on the segments. The book starts by teaching you how to use Python libraries, such as pandas and Matplotlib, to read data from Python, manipulate it, and create plots, using both categorical and continuous variables. Then, you'll learn how to segment a population into groups and use different clustering techniques to evaluate customer segmentation. As you make your way through the chapters, you'll explore ways to evaluate and select the best segmentation approach, and go on to create a linear regression model on customer value data to predict lifetime value. In the concluding chapters, you'll gain an understanding of regression techniques and tools for evaluating regression models, and explore ways to predict customer choice using classification algorithms. Finally, you'll apply these techniques to create a churn model for modeling customer product choices.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Cross-entropy is commonly used in machine learning as a loss function. Cross-entropy is a measure from the field of information theory, building upon entropy and generally calculating the difference between two probability distributions. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions. Cross-entropy is also related to and often confused with logistic loss, called log loss. Although the two measures are derived from a different source, when used as loss functions for classification models, both measures calculate the same quantity and can be used interchangeably. In this tutorial, you will discover cross-entropy for machine learning.

Question Can machine learning algorithms identify oncology patients at risk of short-term mortality to inform timely conversations between patients and physicians regrading serious illness? Findings In this cohort study of 26 525 patients seen in oncology practices within a large academic health system, machine learning algorithms accurately identified patients at high risk of 6-month mortality with good discrimination and positive predictive value. When the gradient boosting algorithm was applied in real time, most patients who were classified as having high risk were deemed appropriate by oncology clinicians for a conversation regarding serious illness. Meaning In this study, machine learning algorithms accurately identified patients with cancer who were at risk of 6-month mortality, suggesting that these models could facilitate more timely conversations between patients and physicians regarding goals and values. Importance Machine learning algorithms could identify patients with cancer who are at risk of short-term mortality. However, it is unclear how different machine learning algorithms compare and whether they could prompt clinicians to have timely conversations about treatment and end-of-life preferences. Objectives To develop, validate, and compare machine learning algorithms that use structured electronic health record data before a clinic visit to predict mortality among patients with cancer. Design, Setting, and Participants Cohort study of 26 525 adult patients who had outpatient oncology or hematology/oncology encounters at a large academic cancer center and 10 affiliated community practices between February 1, 2016, and July 1, 2016.

Humans learn from past experiences, computers learn from previous data.

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of two independent processes: one in the subspace spanned by the inducing basis and the other in the orthogonal complement to this subspace. We show that this formulation recovers existing approximations and at the same time allows to obtain tighter lower bounds on the marginal likelihood and new stochastic variational inference algorithms. We demonstrate the efficiency of these algorithms in several Gaussian process models ranging from standard regression to multi-class classification using (deep) convo-lutional Gaussian processes and report state-of-the-art results on CIF AR-10 with purely GPbased models.

Sports competitions are widely researched in computer and social science, with the goal of understanding how players act under uncertainty. While there is an abundance of computational work on player metrics prediction based on past performance, very few attempts to incorporate out-of-game signals have been made. Specifically, it was previously unclear whether linguistic signals gathered from players' interviews can add information which does not appear in performance metrics. To bridge that gap, we define text classification tasks of predicting deviations from mean in NBA players' in-game actions, which are associated with strategic choices, player behavior and risk, using their choice of language prior to the game. We collected a dataset of transcripts from key NBA players' pre-game interviews and their in-game performance metrics, totaling in 5,226 interview-metric pairs. We design neural models for players' action prediction based on increasingly more complex aspects of the language signals in their open-ended interviews. Our models can make their predictions based on the textual signal alone, or on a combination with signals from past-performance metrics. Our text-based models outperform strong baselines trained on performance metrics only, demonstrating the importance of language usage for action prediction. Moreover, the models that employ both textual input and past-performance metrics produced the best results. Finally, as neural networks are notoriously difficult to interpret, we propose a method for gaining further insight into what our models have learned. Particularly, we present an LDA-based analysis, where we interpret model predictions in terms of correlated topics. We find that our best performing textual model is most associated with topics that are intuitively related to each prediction task and that better models yield higher correlation with more informative topics.

In this post we will talk about applying gradient descent on \(m\) training examples. Now the question is how we can define what gradient descent is? A gradient descent is an efficient optimization algorithm that attempts to find a global minimum of a function. It also enables a model to calculate the gradient or direction that the model should take to reduce errors (differences between actual \(y\) and predicted \(\hat{y}\)). Now let's remind ourselves what the cost function is?