In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved when a model is expressive enough to capture trends in the data, yet not so complex that it overfits idiosyncratic features of the training data. Recently, it has become clear that this classic understanding of the bias-variance must be fundamentally revisited in light of the incredible predictive performance of "overparameterized models" -- models that avoid overfitting even when the number of fit parameters is large enough to perfectly fit the training data. Here, we present results for one of the simplest examples of an overparameterized model: regression with random linear features (i.e. a two-layer neural network with a linear activation function). Using the zero-temperature cavity method, we derive analytic expressions for the training error, test error, bias, and variance. We show that the linear random features model exhibits three phase transitions: two different transitions to an interpolation regime where the training error is zero, along with an additional transition between regimes with large bias and minimal bias. Using random matrix theory, we show how each transition arises due to small nonzero eigenvalues in the Hessian matrix. Finally, we compare and contrast the phase diagram of the random linear features model to the random nonlinear features model and ordinary regression, highlighting the new phase transitions that result from the use of linear basis functions.

I will walk you through this process using OSEMN framework, which covers every step of the data science project lifecycle from end to end. The very first step of a data science project is straightforward. We obtain the data that we need from available data sources. In this step, you will need to query databases, using technical skills like MySQL to process the data. You may also receive data in file formats like Microsoft Excel.

The easiest way to distinguish a supervised learning and unsupervised learning is to see whether the data is labelled or not. Supervised learning learns a function to make prediction of a defined label based on the input data. It can be either classifying data into a category (classification problem) or forecasting an outcome (regression algorithms). Reinforcement learning is another type of machine learning, where the agents learn to take actions based on its interaction with the environment, with the aim to maximize rewards. It is most similar to the learning process of human, following a trial-and-error approach.

Apply advanced machine learning models to perform sentiment analysis and classify customer reviews such as Amazon Alexa products reviews Understand the theory and intuition behind several machine learning algorithms such as K-Nearest Neighbors, Support Vector Machines (SVM), Decision Trees, Random Forest, Naive Bayes, and Logistic Regression Implement classification algorithms in Scikit-Learn for K-Nearest Neighbors, Support Vector Machines (SVM), Decision Trees, Random Forest, Naive Bayes, and Logistic Regression Build an e-mail spam classifier using Naive Bayes classification Technique Apply machine learning models to Healthcare applications such as Cancer and Kyphosis diseases classification Develop Models to predict customer behavior towards targeted Facebook Ads Classify data using K-Nearest Neighbors, Support Vector Machines (SVM), Decision Trees, Random Forest, Naive Bayes, and Logistic Regression Build an in-store feature to predict customer's size using their features Develop a fraud detection classifier using Machine Learning Techniques Master Python Seaborn library for statistical plots Understand the difference between Machine Learning, Deep Learning and Artificial Intelligence Perform feature engineering and clean your training and testing data to remove outliers Master Python and Scikit-Learn for Data Science and Machine Learning Learn to use Python Matplotlib library for data Plotting Build an in-store feature to predict customer's size using their features Are you ready to master Machine Learning techniques and Kick-off your career as a Data Scientist?! You came to the right place! Machine Learning skill is one of the top skills to acquire in 2019 with an average salary of over $114,000 in the United States according to PayScale! The total number of ML jobs over the past two years has grown around 600 percent and expected to grow even more by 2020. In this course, we are going to provide students with knowledge of key aspects of state-of-the-art classification techniques.

Automatic passenger counting (APC) in public transportation has been approached with various machine learning and artificial intelligence methods since its introduction in the 1970s. While equivalence testing is becoming more popular than difference detection (Student's t-test), the former is much more difficult to pass to ensure low user risk. On the other hand, recent developments in artificial intelligence have led to algorithms that promise much higher counting quality (lower bias). However, gradient-based methods (including Deep Learning) have one limitation: they typically run into local optima. In this work, we explore and exploit various aspects of machine learning to increase reliability, performance, and counting quality. We perform a grid search with several fundamental parameters: the selection and size of the training set, which is similar to cross-validation, and the initial network weights and randomness during the training process. Using this experiment, we show how aggregation techniques such as ensemble quantiles can reduce bias, and we give an idea of the overall spread of the results. We utilize the test success chance, a simulative metric based on the empirical distribution. We also employ a post-training Monte Carlo quantization approach and introduce cumulative summation to turn counting into a stationary method and allow unbounded counts.

Purpose: To explore the potential of Explainable Machine Learning in the prediction and detection of drivers of cleared homicides at the national- and state-levels in the United States. Methods: First, nine algorithmic approaches are compared to assess the best performance in predicting cleared homicides country-wise, using data from the Murder Accountability Project. The most accurate algorithm among all (XGBoost) is then used for predicting clearance outcomes state-wise. Second, SHAP, a framework for Explainable Artificial Intelligence, is employed to capture the most important features in explaining clearance patterns both at the national and state levels. Results: At the national level, XGBoost demonstrates to achieve the best performance overall. Substantial predictive variability is detected state-wise. In terms of explainability, SHAP highlights the relevance of several features in consistently predicting investigation outcomes. These include homicide circumstances, weapons, victims' sex and race, as well as number of involved offenders and victims. Conclusions: Explainable Machine Learning demonstrates to be a helpful framework for predicting homicide clearance. SHAP outcomes suggest a more organic integration of the two theoretical perspectives emerged in the literature. Furthermore, jurisdictional heterogeneity highlights the importance of developing ad hoc state-level strategies to improve police performance in clearing homicides.

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named linearFGW, defined as the Euclidean distance between their embeddings. The advantages of the proposed distance are twofold: 1) it can take into account node feature and structure of graphs for measuring the similarity between graphs in a kernel-based framework, 2) it can be much faster for computing kernel matrix than pairwise OT-based distances, particularly fused Gromov-Wasserstein, making it possible to deal with large-scale data sets. After discussing theoretical properties of linearFGW, we demonstrate experimental results on classification and clustering tasks, showing the effectiveness of the proposed linearFGW.

Constructing accurate and generalizable approximators for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. We demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of input functions and output QoIs. To enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations and $\mathcal{O}(\nu n)$ storage. This leads to a linear-cost solver since $\nu$ is chosen to be fixed and usually very small in most applications. The proposed method can be applied to multi-dimensional problems if a full grid or a sparse grid design is used. The proposed method is based on a novel theory for Mat\'ern correlation functions. We find that a suitable rearrangement of these correlation functions can produce a compactly supported function, called a "kernel packet". Using a set of kernel packets as basis functions leads to a sparse representation of the covariance matrix that results in the proposed algorithm. Simulation studies show that the proposed algorithm, when applicable, is significantly superior to the existing alternatives in both the computational time and predictive accuracy.

Recent advancements in deep reinforcement learning have brought forth an impressive display of highly skilled artificial agents capable of complex intelligent behavior. In video games, these artificial agents are increasingly deployed as non-playable characters (NPCs) designed to enhance the experience of human players. However, while it has been shown that the convincing human-like behavior of NPCs leads to increased engagement in video games, the believability of an artificial agent's behavior is most often measured solely by its proficiency at a given task. Recent work has hinted that proficiency alone is not sufficient to discern human-like behavior. Motivated by this, we build a non-parametric two-sample hypothesis test designed to compare the behaviors of artificial agents to those of human players. We show that the resulting $p$-value not only aligns with anonymous human judgment of human-like behavior, but also that it can be used as a measure of similarity.