We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on K\"ahler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi-Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.

Current clinical practice guidelines for managing Coronary Artery Disease (CAD) account for general cardiovascular risk factors. However, they do not present a framework that considers personalized patient-specific characteristics. Using the electronic health records of 21,460 patients, we created data-driven models for personalized CAD management that significantly improve health outcomes relative to the standard of care. We develop binary classifiers to detect whether a patient will experience an adverse event due to CAD within a 10-year time frame. Combining the patients' medical history and clinical examination results, we achieve 81.5% AUC. For each treatment, we also create a series of regression models that are based on different supervised machine learning algorithms. We are able to estimate with average R squared = 0.801 the time from diagnosis to a potential adverse event (TAE) and gain accurate approximations of the counterfactual treatment effects. Leveraging combinations of these models, we present ML4CAD, a novel personalized prescriptive algorithm. Considering the recommendations of multiple predictive models at once, ML4CAD identifies for every patient the therapy with the best expected outcome using a voting mechanism. We evaluate its performance by measuring the prescription effectiveness and robustness under alternative ground truths. We show that our methodology improves the expected TAE upon the current baseline by 24.11%, increasing it from 4.56 to 5.66 years. The algorithm performs particularly well for the male (24.3% improvement) and Hispanic (58.41% improvement) subpopulations. Finally, we create an interactive interface, providing physicians with an intuitive, accurate, readily implementable, and effective tool.

Modal regression is aimed at estimating the global mode (i.e., global maximum) of the conditional density function of the output variable given input variables, and has led to regression methods robust against heavy-tailed or skewed noises. The conditional mode is often estimated through maximization of the modal regression risk (MRR). In order to apply a gradient method for the maximization, the fundamental challenge is accurate approximation of the gradient of MRR, not MRR itself. To overcome this challenge, in this paper, we take a novel approach of directly approximating the gradient of MRR. To approximate the gradient, we develop kernelized and neural-network-based versions of the least-squares log-density derivative estimator, which directly approximates the derivative of the log-density without density estimation. With direct approximation of the MRR gradient, we first propose a modal regression method with kernels, and derive a new parameter update rule based on a fixed-point method. Then, the derived update rule is theoretically proved to have a monotonic hill-climbing property towards the conditional mode. Furthermore, we indicate that our approach of directly approximating the gradient is compatible with recent sophisticated stochastic gradient methods (e.g., Adam), and then propose another modal regression method based on neural networks. Finally, the superior performance of the proposed methods is demonstrated on various artificial and benchmark datasets.

I strongly advise you to read the article linked above. It will set the foundations on the topic, plus some math is already discussed there. To start out, I'll define my dataset -- only three points that are in a linear relationship. I've chosen so few points only because the math will be shorter -- needless to say, the math won't be more complex for longer dataset, it would just be longer, and I don't want to make some stupid arithmetic mistake. Then I'll set coefficients beta 0 and beta 1 to some constant and define the cost function as Sum of Squared Residuals (SSR/SSE).

Fresh off of the OpenAI Retro contest, I wanted to keep exploring more AI topics. Somebody told me that the best way to learn was reproducing other people's papers, but not wanting to learn any more Python than I had to, I decided to try to tackle some existing work with TensorFlow.js. I first tried to run with a GAN, but I realized it might be better to crawl first since I am coming from a pretty fresh background. I was able to find a series of basic TensorFlow examples that I felt would let me ladder up my TensorFlow.js I'll be redoing all of these Basic Operations and Linear Regressionwith TensorFlow.js.

We conduct a large-scale benchmark experiment aiming to advance the use of machine-learning quantile regression algorithms for probabilistic hydrological post-processing "at scale" within operational contexts. The experiment is set up using 34-year-long daily time series of precipitation, temperature, evapotranspiration and streamflow for 511 catchments over the contiguous United States. Point hydrological predictions are obtained using the Génie Rural à 4 paramètres Journalier (GR4J) hydrological model and exploited as predictor variables within quantile regression settings. Six machine-learning quantile regression algorithms and their equal-weight combiner are applied to predict conditional quantiles of the hydrological model errors. The individual algorithms are quantile regression, generalized random forests for quantile regression, generalized random forests for quantile regression emulating quantile regression forests, gradient boosting machine, model-based boosting with linear models as base learners and quantile regression neural networks.

Television is an ever-evolving multi billion dollar industry. The success of a television show in an increasingly technological society is a vast multi-variable formula. The art of success is not just something that happens, but is studied, replicated, and applied. Hollywood can be unpredictable regarding success, as many movies and sitcoms that are hyped up and promise to be a hit end up being box office failures and complete disappointments. In current studies, linguistic exploration is being performed on the relationship between Television series and target community of viewers. Having a decision support system that can display sound and predictable results would be needed to build confidence in the investment of a new TV series. The models presented in this study use data to study and determine what makes a sitcom successful. In this paper, we use descriptive and predictive modeling techniques to assess the continuing success of television comedies: The Office, Big Bang Theory, Arrested Development, Scrubs, and South Park. The factors that are tested for statistical significance on episode ratings are character presence, director, and writer. These statistics show that while characters are indeed crucial to the shows themselves, the creation and direction of the shows pose implication upon the ratings and therefore the success of the shows. We use machine learning based forecasting models to accurately predict the success of shows. The models represent a baseline to understanding the success of a television show and how producers can increase the success of current television shows or utilize this data in the creation of future shows. Due to the many factors that go into a series, the empirical analysis in this work shows that there is no one-fits-all model to forecast the rating or success of a television show.

After modeling, the next stage is always analyzing how our model is performing and why it is doing what it's doing. However, if you've had the chance to work with ensemble methods, you probably already know that these algorithms are usually known as "black-box models". These models lack explicability and interpretability since the way they usually work implies one or several layers of a machine making decisions without human supervision, apart from a group of rules or parameters set. More often than not, not even the most expert professionals in the field can understand the function that is actually created by, for example, training a neural network. In this sense, some of the most classical machine learning models were actually better. That's why, for the sake of this post, we'll be analyzing the feature importance of our project using a classic Logistic Regression.

A recent Forbes article [41] states that "Machine learning algorithms are very dependent on accurate, clean, and well-labeled training data to learn from so that they can produce accurate results" and "According to a recent report from AI research and advisory firm Cognilytica, over 80% of the time spent in AI projects are spent dealing with and wrangling data." While some abnormal samples, or outliers, can be detected and filtered during the preprocessing steps, others are more difficult to detect: for instance, a sophisticated adversary might try to "poison" data to force a desired outcome [33]. Other seemingly abnormal observations could be inherent to the underlying data-generating process. An "ideal" learning method should not discard informative samples, while limiting the effect of individual observation on the output of the learning algorithm at the same time. We are interested in robust methods that are model-free, and require minimal assumptions on the underlying distribution. We study two types of robustness: robustness to heavy tails expressed in terms of the moment requirements, as well as robustness to adversarial contamination. Heavy tails can be used to model variation and randomness naturally occurring in the sample, while adversarial contamination is a convenient way to model outliers of unknown nature. The statistical framework used throughout the paper is defined as follows. Let p S, S q be a measurable space, and let X P S be a random variable with distribution P .

We introduce a new meta-learning procedure, called non-Euclidean upgrading (NEU), which learns algorithm-specific geometries by deforming the ambient space until the algorithm can achieve optimal performance. We prove that these deformations have several novel and semi-classical universal approximation properties. These deformations can be used to approximate any continuous, Borel, or modular-Lebesgue integrable functions to arbitrary precision. Further, these deformations can transport any data-set into any other data-set in a finite number of iterations while leaving most of the space fixed. The NEU meta-algorithm embeds these deformations into a wide range of learning algorithms. We prove that the NEU version of the original algorithm must perform better than the original learning algorithm. Moreover, by quantifying model-free learning algorithms as specific unconstrained optimization problems, we find that the NEU version of a learning algorithm must perform better than the model-free extension of the original algorithm. The properties and performance of the NEU meta-algorithm are examined in various simulation studies and applications to financial data.