We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage consumption and computational complexity. Furthermore, the method can be regarded as a regularization technique, which improves the generalizability of learned target functions. We demonstrate significant improvements in comparison to the computation of data-driven predictions involving the full training data set. The method is applied to classification and regression problems from different application areas such as image recognition, system identification, and oceanographic time series analysis.

This course is targeted for Beginner Python Developers who want to kickstart their journey in Machine Learning. In this course, we are going to use a linear regression model from scikit-learn library in Python to predict the total no. of positive cases for COVID19 in a particular state in India. After completing this course, you'll be able to:

Normal Distribution is an important concept in statistics and the backbone of Machine Learning. A Data Scientist needs to know about Normal Distribution when they work with Linear Models(perform well if the data is normally distributed), Central Limit Theorem, and exploratory data analysis. As discovered by Carl Friedrich Gauss, Normal Distribution/Gaussian Distribution is a continuous probability distribution. It has a bell-shaped curve that is symmetrical from the mean point to both halves of the curve. A continuous random variable "x" is said to follow a normal distribution with parameter μ(mean) and σ(standard deviation), if it's probability density function is given by, This is also called a normal variate.

Before we dive into the Airbnb dataset and our findings, let's do an in-depth review of the K-Means clustering algorithm. An unsupervised learner receives unlabeled training data and makes predictions for unseen points. Clustering analysis falls under unsupervised learning. A cluster is a collection of data objects that are similar (or related) to one another within the same group, or dissimilar (or unrelated) to the objects in other groups. "Good" clusters will have the following: high intra-class similarity (cohesiveness within clusters) and low inter-class similarity (distinctive between clusters). The K-Means algorithm is common a type of clustering analysis.

In this section we will learn - What does Machine Learning mean. What are the meanings or different terms associated with machine learning? You will see some examples so that you understand what machine learning actually is. It also contains steps involved in building a machine learning model, not just linear models, any machine learning model.

Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by linear least squares regression. Hence, the choice of basis functions is crucial for the accuracy of the method. Earlier work by some of us [Belomestny, Schoenmakers, Spokoiny, Zharkynbay. Commun.~Math.~Sci., 18(1):109-121, 2020] proposes to \emph{reinforce} the basis functions in the case of optimal stopping problems by already computed value functions for later times, thereby considerably improving the accuracy with limited additional computational cost. We extend the reinforced regression method to a general class of stochastic control problems, while considerably improving the method's efficiency, as demonstrated by substantial numerical examples as well as theoretical analysis.

Time series classification (TSC) gained a lot of attention in the past decade and number of methods for representing and classifying time series have been proposed. Nowadays, methods based on convolutional networks and ensemble techniques represent the state of the art for time series classification. Techniques transforming time series to image or text also provide reliable ways to extract meaningful features or representations of time series. We compare the state-of-the-art representation and classification methods on a specific application, that is predictive maintenance from sequences of event logs. The contributions of this paper are twofold: introducing a new data set for predictive maintenance on automated teller machines (ATMs) log data and comparing the performance of different representation methods for predicting the occurrence of a breakdown. The problem is difficult since unlike the classic case of predictive maintenance via signals from sensors, we have sequences of discrete event logs occurring at any time and the lengths of the sequences, corresponding to life cycles, vary a lot.

Distinguishing COVID-19 from other flu-like illnesses can be difficult due to ambiguous symptoms and still an initial experience of doctors. Whereas, it is crucial to filter out those sick patients who do not need to be tested for SARS-CoV-2 infection, especially in the event of the overwhelming increase in disease. As a part of the presented research, logistic regression and XGBoost classifiers, that allow for effective screening of patients for COVID-19, were generated. Each of the methods was tuned to achieve an assumed acceptable threshold of negative predictive values during classification. Additionally, an explanation of the obtained classification models was presented. The explanation enables the users to understand what was the basis of the decision made by the model. The obtained classification models provided the basis for the DECODE service (decode.polsl.pl), which can serve as support in screening patients with COVID-19 disease. Moreover, the data set constituting the basis for the analyses performed is made available to the research community. This data set consisting of more than 3,000 examples is based on questionnaires collected at a hospital in Poland.

Age estimation has attracted attention for its various medical applications. There are many studies on human age estimation from biomedical images. However, there is no research done on mammograms for age estimation, as far as we know. The purpose of this study is to devise an AI-based model for estimating age from mammogram images. Due to lack of public mammography data sets that have the age attribute, we resort to using a web crawler to download thumbnail mammographic images and their age fields from the public data set; the Digital Database for Screening Mammography. The original images in this data set unfortunately can only be retrieved by a software which is broken. Subsequently, we extracted deep learning features from the collected data set, by which we built a model using Random Forests regressor to estimate the age automatically. The performance assessment was measured using the mean absolute error values. The average error value out of 10 tests on random selection of samples was around 8 years. In this paper, we show the merits of this approach to fill up missing age values. We ran logistic and linear regression models on another independent data set to further validate the advantage of our proposed work. This paper also introduces the free-access Mini-DDSM data set.

Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In reality, the cost of evaluating different hyperparameters, be it in terms of time, dollars or energy, can span several orders of magnitude of difference. While a number of heuristics have been proposed to make BO cost-aware, none of these have been proven to work robustly. In this work, we reformulate cost-aware BO in terms of Pareto efficiency and introduce the cost Pareto Front, a mathematical object allowing us to highlight the shortcomings of commonly used acquisition functions. Based on this, we propose a novel Pareto-efficient adaptation of the expected improvement. On 144 real-world black-box function optimization problems we show that our Pareto-efficient acquisition functions significantly outperform previous solutions, bringing up to 50% speed-ups while providing finer control over the cost-accuracy trade-off. We also revisit the common choice of Gaussian process cost models, showing that simple, low-variance cost models predict training times effectively.