A prediction interval is calculated as some combination of the estimated variance of the model and the variance of the outcome variable. Prediction intervals are easy to describe, but difficult to calculate in practice. In simple cases like linear regression, we can estimate the confidence interval directly. In the cases of nonlinear regression algorithms, such as artificial neural networks, it is a lot more challenging and requires the choice and implementation of specialized techniques. General techniques such as the bootstrap resampling method can be used, but are computationally expensive to calculate. The paper "A Comprehensive Review of Neural Network-based Prediction Intervals and New Advances" provides a reasonably recent study of prediction intervals for nonlinear models in the context of neural networks.

The common perception of machine learning is that it starts with data and ends with a model. In real-world production systems, the traditional data science and machine learning workflow of data preparation, feature engineering, and model selection, while important, is just one aspect. A critical missing piece is the deployment and management of models, as well as the integration between the model creation and deployment phases. This is particularly challenging in the case of deploying Apache Spark ML pipelines for low latency scoring. While MLlib's DataFrame API is powerful, elegant, and works well in batch scoring scenarios, it is relatively ill-suited to the needs of many real-time predictive applications, for two main reasons.

A measure of relative importance of variables is often desired by researchers when the explanatory aspects of econometric methods are of interest. To this end, the author briefly reviews the limitations of conventional econometrics in constructing a reliable measure of variable importance. The author highlights the relative stature of explanatory and predictive analysis in economics and the emergence of fruitful collaborations between econometrics and computer science. Learning lessons from both, the author proposes a hybrid approach based on conventional econometrics and advanced machine learning (ML) algorithms, which are otherwise, used in predictive analytics. The purpose of this article is two-fold, to propose a hybrid approach to assess relative importance and demonstrate its applicability in addressing policy priority issues with an example of food inflation in India, followed by a broader aim to introduce the possibility of conflation of ML and conventional econometrics to an audience of researchers in economics and social sciences, in general.

We provide theoretical investigation of curriculum learning in the context of stochastic gradient descent when optimizing the convex linear regression loss. We prove that the rate of convergence of an ideal curriculum learning method is monotonically increasing with the difficulty of the examples. Moreover, among all equally difficult points, convergence is faster when using points which incur higher loss with respect to the current hypothesis. We then analyze curriculum learning in the context of training a CNN. We describe a method which infers the curriculum by way of transfer learning from another network, pre-trained on a different task. While this approach can only approximate the ideal curriculum, we observe empirically similar behavior to the one predicted by the theory, namely, a significant boost in convergence speed at the beginning of training. When the task is made more difficult, improvement in generalization performance is also observed. Finally, curriculum learning exhibits robustness against unfavorable conditions such as excessive regularization.

Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm is introduced to address this expected risk minimization problem. Though it converges faster than SGD, a significant amount of memory is required. In this pa- per, we propose two SGD-like algorithms for expected risk minimization with random perturbation, namely, stochastic sample average gradient (SSAG) and stochastic SAGA (S-SAGA). The memory cost of SSAG does not depend on the sample size, while that of S-SAGA is the same as those of variance reduction methods on un- perturbed data. Theoretical analysis and experimental results on logistic regression and AUC maximization show that SSAG has faster convergence rate than SGD with comparable space requirement, while S-SAGA outperforms S-MISO in terms of both iteration complexity and storage.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than the standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

Missing responses is a missing data format in which outcomes are not always observed. In this work we develop kernel machines that can handle missing responses. First, we propose a kernel machine family that uses mainly the complete cases. For the quadratic loss, we then propose a family of doubly-robust kernel machines. The proposed kernel-machine estimators can be applied to both regression and classification problems. We prove oracle inequalities for the finite-sample differences between the kernel machine risk and Bayes risk. We use these oracle inequalities to prove consistency and to calculate convergence rates. We demonstrate the performance of the two proposed kernel machine families using both a simulation study and a real-world data analysis.

Randomized trials, also known as A/B tests, are used to select between two policies: a control and a treatment. Given a corresponding set of features, we can ideally learn an optimized policy P that maps the A/B test data features to action space and optimizes reward. However, although A/B testing provides an unbiased estimator for the value of deploying B (i.e., switching from policy A to B), direct application of those samples to learn the the optimized policy P generally does not provide an unbiased estimator of the value of P as the samples were observed when constructing P. In situations where the cost and risks associated of deploying a policy are high, such an unbiased estimator is highly desirable. We present a procedure for learning optimized policies and getting unbiased estimates for the value of deploying them. We wrap any policy learning procedure with a bagging process and obtain out-of-bag policy inclusion decisions for each sample. We then prove that inverse-propensity-weighting effect estimator is unbiased when applied to the optimized subset. Likewise, we apply the same idea to obtain out-of-bag unbiased per-sample value estimate of the measurement that is independent of the randomized treatment, and use these estimates to build an unbiased doubly-robust effect estimator. Lastly, we empirically shown that even when the average treatment effect is negative we can find a positive optimized policy.

Edwin V. Bonilla School of Computer Science and Engineering University of New South Wales Sydney, Australia We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of developing scalable methods for distributed solar power forecasting, we propose coupled priors over groups of (node or weight) processes to estimate a forecast model for solar power production at multiple distributed sites, exploiting spatial dependence between functions. Our results show that our approach provides better quantification of predictive uncertainties than competing benchmarks while maintaining high point-prediction accuracy.

This article targets whom have a basic understanding for TensorFlow Core API. Learning TensorFlow Core API, which is the lowest level API in TensorFlow, is a very good step for starting learning TensorFlow because it let you understand the kernel of the library. Here is a very simple example of TensorFlow Core API in which we create and train a linear regression model. The loss returned is 53.76. Existence of error, specially for large error, means that the parameters used must be updated.