These days I am having several interviews in the field of Machine Learning as I have moved abroad and need to look for a new job. Big companies and small startups always want to make sure you know the fundamentals of Machine Learning, and so I'm using some of my time going over the basics again. So I decided to share a series of articles about what you need to know to deal with interviews in Machine Learning hoping it will help some of you as well. When we talk about Linear Regression, we have a set of points that for ease you can think of plotted on a plane in 2 dimensions (x: feature, y: label) and we want to fit these points with a straight line. That is, we want to find that straight line that passes right'between' the points as in the figure above.

A characteristic feature of time-to-event data analysis is possible censoring of the event time. Most of the statistical learning methods for handling censored data are limited by the assumption of independent censoring, even if this can lead to biased predictions when the assumption does not hold. This paper introduces Clayton-boost, a boosting approach built upon the accelerated failure time model, which uses a Clayton copula to handle the dependency between the event and censoring distributions. By taking advantage of a copula, the independent censoring assumption is not needed any more. During comparisons with commonly used methods, Clayton-boost shows a strong ability to remove prediction bias at the presence of dependent censoring and outperforms the comparing methods either if the dependency strength or percentage censoring are considerable. The encouraging performance of Clayton-boost shows that there is indeed reasons to be critical about the independent censoring assumption, and that real-world data could highly benefit from modelling the potential dependency.

Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are limited methods for high-dimensional covariates with measurement error, that usually require knowledge of the noise distribution and focus on linear or generalized linear models. In this work, we develop high-dimensional measurement error models for a class of Lipschitz loss functions that encompasses logistic regression, hinge loss and quantile regression, among others. Our estimator is designed to minimize the $L_1$ norm among all estimators belonging to suitable feasible sets, without requiring any knowledge of the noise distribution. Subsequently, we generalize these estimators to a Lasso analog version that is computationally scalable to higher dimensions. We derive theoretical guarantees in terms of finite sample statistical error bounds and sign consistency, even when the dimensionality increases exponentially with the sample size. Extensive simulation studies demonstrate superior performance compared to existing methods in classification and quantile regression problems. An application to a gender classification task based on brain functional connectivity in the Human Connectome Project data illustrates improved accuracy under our approach, and the ability to reliably identify significant brain connections that drive gender differences.

Analytics of financial data is inherently a Big Data paradigm, as such data are collected over many assets, asset classes, countries, and time periods. This represents a challenge for modern machine learning models, as the number of model parameters needed to process such data grows exponentially with the data dimensions; an effect known as the Curse-of-Dimensionality. Recently, Tensor Decomposition (TD) techniques have shown promising results in reducing the computational costs associated with large-dimensional financial models while achieving comparable performance. However, tensor models are often unable to incorporate the underlying economic domain knowledge. To this end, we develop a novel Graph-Regularized Tensor Regression (GRTR) framework, whereby knowledge about cross-asset relations is incorporated into the model in the form of a graph Laplacian matrix. This is then used as a regularization tool to promote an economically meaningful structure within the model parameters. By virtue of tensor algebra, the proposed framework is shown to be fully interpretable, both coefficient-wise and dimension-wise. The GRTR model is validated in a multi-way financial forecasting setting and compared against competing models, and is shown to achieve improved performance at reduced computational costs. Detailed visualizations are provided to help the reader gain an intuitive understanding of the employed tensor operations.

Vertical federated learning (VFL), where data features are stored in multiple parties distributively, is an important area in machine learning. However, the communication complexity for VFL is typically very high. In this paper, we propose a unified framework by constructing coresets in a distributed fashion for communication-efficient VFL. We study two important learning tasks in the VFL setting: regularized linear regression and $k$-means clustering, and apply our coreset framework to both problems. We theoretically show that using coresets can drastically alleviate the communication complexity, while nearly maintain the solution quality. Numerical experiments are conducted to corroborate our theoretical findings.

Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in this paper we caution against a strong inductive bias for interpolation in the presence of noise: While a stronger inductive bias encourages a simpler structure that is more aligned with the ground truth, it also increases the detrimental effect of noise. Specifically, for both linear regression and classification with a sparse ground truth, we prove that minimum $\ell_p$-norm and maximum $\ell_p$-margin interpolators achieve fast polynomial rates close to order $1/n$ for $p > 1$ compared to a logarithmic rate for $p = 1$. Finally, we provide preliminary experimental evidence that this trade-off may also play a crucial role in understanding non-linear interpolating models used in practice.

Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing amount of information around us, calculating similarity becomes increasingly complex, especially in many cases, such as legal or medical affairs, measuring similarity requires extra care and precision, as small acts within a language unit can have significant real-world effects. My research goal in this thesis is to develop regression models that account for similarities between language units in a more refined way. Computation of similarity has come a long way, but approaches to debugging the measures are often based on continually fitting human judgment values. To this end, my goal is to develop an algorithm that precisely catches loopholes in a similarity calculation. Furthermore, most methods have vague definitions of the similarities they compute and are often difficult to interpret. The proposed framework addresses both shortcomings. It constantly improves the model through catching different loopholes. In addition, every refinement of the model provides a reasonable explanation. The regression model introduced in this thesis is called progressively refined similarity computation, which combines attack testing with adversarial training. The similarity regression model of this thesis achieves state-of-the-art performance in handling edge cases.

Word order choices during sentence production can be primed by preceding sentences. In this work, we test the DUAL MECHANISM hypothesis that priming is driven by multiple different sources. Using a Hindi corpus of text productions, we model lexical priming with an n-gram cache model and we capture more abstract syntactic priming with an adaptive neural language model. We permute the preverbal constituents of corpus sentences, and then use a logistic regression model to predict which sentences actually occurred in the corpus against artificially generated meaning-equivalent variants. Our results indicate that lexical priming and lexically-independent syntactic priming affect complementary sets of verb classes. By showing that different priming influences are separable from one another, our results support the hypothesis that multiple different cognitive mechanisms underlie priming.

Create a regressor and call it, 'poly_reg'. Assign the regressor to the lm() function as we did in linear regression. The function takes two arguments. The formula and the data, same way we did in linear regression. To transform this from a linear regression to a polynomial regression model, we need to add some polynomial features.

We are going to learn how to implement a Multiple Linear Regression model in R. This is a bit more complex than Simple Linear Regression but it's going to be so practical and fun. Multiple Linear Regression is a data science technique that uses several explanatory variables to predict the outcome of a response variable. A Multiple linear regression model attempts to model the relationship between two or more explanatory variables (independent variables) and a response variable (dependent variable), by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y.