CS 229 ― Machine Learning My twin brother Afshine and I created this set of illustrated Machine Learning cheatsheets covering the content of the CS 229 class, which I TA-ed in Fall 2018 at Stanford. They can (hopefully!) be useful to all future students of this course as well as to anyone else interested in Machine Learning.

Linear regression is the most basic and the most widely used technique in machine learning; yet for all its simplicity, studying it can unlock some of the most important concepts in statistics. If you have a basic undestanding of linear regression expressed as $ \hat{Y} \theta_0 \theta_1X$, but don't have a background in statistics and find statements like "ridge regression is equivalent to the maximum a posteriori (MAP) estimate with a zero-mean Gaussian prior" bewildering, then this post is for you. With a superficial goal of understanding that somewhat obtuse statement, its main objective is to explore the topic, starting from the standard formulation of linear regression, moving on to the probabilistic approach (maximum likelihood formulation) and from there to Bayesian linear regression. I'll use the $\theta$ character throughout to refer to the coefficients (weights) of a regression model, either explicitly broken out as $\theta_0$ and $\theta_1$ for intercept and slope respectively, or just $\theta$ referring to the vector of coefficients. I'll usually use the expression $\theta Tx_i$ for the prediction a model gives at $x_i$, the assumption being that a 1 has been added to the vector of values at $x_i$. 1 In the single predictor case, we know that the least squares fit is the line that minimizes the sum of the squared distances between observed data and predicted values, i.e. it minimizes the Residual Sum of Squares (RSS): These residuals are pretty important in how we reason about our model.

In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that reflect their nature well. We perform a case study with a dataset of rare-earth transition metal crystalline compounds represented using the Orbital Field Matrix descriptor and the Coulomb Matrix descriptor. We perform predictions of the formation energies using k-nearest neighbors regression, ridge regression, and kernel ridge regression. Through detailed analyses of the yield prediction accuracy, we examine the relationship between the characteristics of the material representation and similarity measures, and the complexity of the energy function they can capture. Empirical experiments and theoretical analysis reveal that similarity measures and kernels that minimize the loss of materials distinctiveness improve the prediction performance.

Model robustness has been an important issue, since adding small adversarial perturbations to images is sufficient to drive the model accuracy down to nearly zero. In this paper, we propose a new training objective "Guided Complement Entropy" (GCE) that has dual desirable effects: (a) neutralizing the predicted probabilities of incorrect classes, and (b) maximizing the predicted probability of the ground-truth class, particularly when (a) is achieved. Training with GCE encourages models to learn latent representations where samples of different classes form distinct clusters, which we argue, improves the model robustness against adversarial perturbations. Furthermore, compared with the state-of-the-arts trained with cross-entropy, same models trained with GCE achieve significant improvements on the robustness against white-box adversarial attacks, both with and without adversarial training. When no attack is present, training with GCE also outperforms cross-entropy in terms of model accuracy.

The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. We prove that all of them guarantee regions with exact coverage probabilities and they are strongly consistent.

Machine learning offers remarkable benefits for improving workplaces and working conditions amongst others in the recycling industry. Here e.g. hand-sorting of medium value scrap is labor intensive and requires experienced and skilled workers. On the one hand, they have to be highly concentrated for making proper readings and analyses of the material, but on the other hand, this work is monotonous. Therefore, a machine learning approach is proposed for a quick and reliable automated identification of alloys in the recycling industry, while the mere scrap handling is regarded to be left in the hands of the workers. To this end, a set of twelve tool and high-speed steels from the field were selected to be identified by their spectrum induced by electric arcs. For data acquisition, the optical emission spectrometer Thorlabs CCS 100 was used. Spectra have been post-processed to be fed into the supervised machine learning algorithm. The development of the machine learning software is conducted according to the steps of the VDI 2221 standard method. For programming Python 3 as well as the python-library sklearn were used. By systematic parameter variation, the appropriate machine learning algorithm was selected and validated. Subsequent validation steps showed that the automated identification process using a machine learning approach and the optical emission spectrometry is applicable, reaching a maximum F1 score of 96.9 %. This performance is as good as the performance of a highly trained worker using visual grinding spark identification. The tests were based on a self-generated set of 600 spectra per single alloy (7,200 spectra in total) which were produced using an industry workshop device.

Reinforcement learning algorithms can be used to optimally solve dynamic decision-making and control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as neural networks or basis function expansions, have two main drawbacks: they are black-box models offering no insight in the mappings learned, and they require significant trial and error tuning of their meta-parameters. In this paper, we propose a new approach to constructing smooth value functions by means of symbolic regression. We introduce three off-line methods for finding value functions based on a state transition model: symbolic value iteration, symbolic policy iteration, and a direct solution of the Bellman equation. The methods are illustrated on four nonlinear control problems: velocity control under friction, one-link and two-link pendulum swing-up, and magnetic manipulation. The results show that the value functions not only yield well-performing policies, but also are compact, human-readable and mathematically tractable. This makes them potentially suitable for further analysis of the closed-loop system. A comparison with alternative approaches using neural networks shows that our method constructs well-performing value functions with substantially fewer parameters.

Wide-band Electromagnetic Induction Sensors (WEMI) have been used for a number of years in subsurface detection of explosive hazards. While WEMI sensors have proven effective at localizing objects exhibiting large magnetic responses, detecting objects lacking or containing very low amounts of conductive materials can be challenging. In this paper, we compare a number of target detection algorithms in the literature in terms of detection performance. In the comparison, methods are tested on two real-world data sets: one containing relatively low amounts of ground noise pollution, and the other demonstrating highly-magnetic soil interference. Results are quantitatively evaluated through receiver-operator characteristic (ROC) curves and are used to highlight the strengths and weaknesses of the compared approaches in hand-held explosive hazard detection.

Time series data in the retail world are particularly rich in terms of dimensionality, and these dimensions can be aggregated in groups or hierarchies. Valuable information is nested in these complex structures, which helps to predict the aggregated time series data. From a portfolio of brands under HUUB's monitoring, we selected two to explore their sales behaviour, leveraging the grouping properties of their product structure. Using statistical models, namely SARIMA, to forecast each level of the hierarchy, an optimal combination approach was used to generate more consistent forecasts in the higher levels. Our results show that the proposed methods can indeed capture nested information in the more granular series, helping to improve the forecast accuracy of the aggregated series. The Weighted Least Squares (WLS) method surpasses all other methods proposed in the study, including the Minimum Trace (MinT) reconciliation.

This paper presents Acquisition Thompson Sampling (ATS), a novel algorithm for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function. In order to improve performance for multi-modal tasks, we show that ATS can be combined with existing techniques in order to realize different explore-exploit trade-offs and take into account pending function evaluations. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the competitiveness of our algorithm with two state-of-the-art batch BO methods, and its advantages to classical parallel Thompson Sampling for BO.