Recent extensive numerical experiments in high scale machine learning have allowed to uncover a quite counterintuitive phase transition, as a function of the ratio between the sample size and the number of parameters in the model. As the number of parameters $p$ approaches the sample size $n$, the generalisation error (a.k.a. testing error) increases, but it many cases, it starts decreasing again past the threshold $p=n$. This surprising phenomenon, brought to the theoretical community attention in \cite{belkin2019reconciling}, has been thorougly investigated lately, more specifically for simpler models than deep neural networks, such as the linear model when the parameter is taken to be the minimum norm solution to the least-square problem, mostly in the asymptotic regime when $p$ and $n$ tend to $+\infty$; see e.g. \cite{hastie2019surprises}. In the present paper, we propose a finite sample analysis of non-linear models of \textit{ridge} type, where we investigate the double descent phenomenon for both the \textit{estimation problem} and the prediction problem. Our results show that the double descent phenomenon can be precisely demonstrated in non-linear settings and complements recent works of \cite{bartlett2020benign} and \cite{chinot2020benign}. Our analysis is based on efficient but elementary tools closely related to the continuous Newton method \cite{neuberger2007continuous}.

Recent advances in time series classification have largely focused on methods that either employ deep learning or utilize other machine learning models for feature extraction. Though successful, their power often comes at the requirement of computational complexity. In this paper, we introduce GeoStat representations for time series. GeoStat representations are based off of a generalization of recent methods for trajectory classification, and summarize the information of a time series in terms of comprehensive statistics of (possibly windowed) distributions of easy to compute differential geometric quantities, requiring no dynamic time warping. The features used are intuitive and require minimal parameter tuning. We perform an exhaustive evaluation of GeoStat on a number of real datasets, showing that simple KNN and SVM classifiers trained on these representations exhibit surprising performance relative to modern single model methods requiring significant computational power, achieving state of the art results in many cases. In particular, we show that this methodology achieves good performance on a challenging dataset involving the classification of fishing vessels, where our methods achieve good performance relative to the state of the art despite only having access to approximately two percent of the dataset used in training and evaluating this state of the art.

We study the average $\mbox{CV}_{loo}$ stability of kernel ridge-less regression and derive corresponding risk bounds. We show that the interpolating solution with minimum norm minimizes a bound on $\mbox{CV}_{loo}$ stability, which in turn is controlled by the condition number of the empirical kernel matrix. The latter can be characterized in the asymptotic regime where both the dimension and cardinality of the data go to infinity. Under the assumption of random kernel matrices, the corresponding test error should be expected to follow a double descent curve.

We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the data and the scale can be shown to control their stability through the condition number. Our analysis shows that are different regimes depending on the interplay between the sample size, its dimensions, and the smoothness of the problem. Indeed, when the sample size is less than exponential in the data dimension, then the scale can be chosen so that the learning error decreases. As the sample size becomes larger, the overall error stop decreasing but interestingly the scale can be chosen in such a way that the variance due to noise remains bounded. Our analysis combines, probabilistic results with a number of analytic techniques from interpolation theory.

Incorporating fairness constructs into machine learning algorithms is a topic of much societal importance and recent interest. Clustering, a fundamental task in unsupervised learning that manifests across a number of web data scenarios, has also been subject of attention within fair ML research. In this paper, we develop a novel notion of fairness in clustering, called representativity fairness. Representativity fairness is motivated by the need to alleviate disparity across objects' proximity to their assigned cluster representatives, to aid fairer decision making. We illustrate the importance of representativity fairness in real-world decision making scenarios involving clustering and provide ways of quantifying objects' representativity and fairness over it. We develop a new clustering formulation, RFKM, that targets to optimize for representativity fairness along with clustering quality. Inspired by the $K$-Means framework, RFKM incorporates novel loss terms to formulate an objective function. The RFKM objective and optimization approach guides it towards clustering configurations that yield higher representativity fairness. Through an empirical evaluation over a variety of public datasets, we establish the effectiveness of our method. We illustrate that we are able to significantly improve representativity fairness at only marginal impact to clustering quality.

Federated learning is typically approached as an optimization problem, where the goal is to minimize a global loss function by distributing computation across client devices that possess local data and specify different parts of the global objective. We present an alternative perspective and formulate federated learning as a posterior inference problem, where the goal is to infer a global posterior distribution by having client devices each infer the posterior of their local data. While exact inference is often intractable, this perspective provides a principled way to search for global optima in federated settings. Further, starting with the analysis of federated quadratic objectives, we develop a computation- and communication-efficient approximate posterior inference algorithm -- federated posterior averaging (FedPA). Our algorithm uses MCMC for approximate inference of local posteriors on the clients and efficiently communicates their statistics to the server, where the latter uses them to refine a global estimate of the posterior mode. Finally, we show that FedPA generalizes federated averaging (FedAvg), can similarly benefit from adaptive optimizers, and yields state-of-the-art results on four realistic and challenging benchmarks, converging faster, to better optima.

In this paper, we study the few-shot multi-label classification for user intent detection. For multi-label intent detection, state-of-the-art work estimates label-instance relevance scores and uses a threshold to select multiple associated intent labels. To determine appropriate thresholds with only a few examples, we first learn universal thresholding experience on data-rich domains, and then adapt the thresholds to certain few-shot domains with a calibration based on nonparametric learning. For better calculation of label-instance relevance score, we introduce label name embedding as anchor points in representation space, which refines representations of different classes to be well-separated from each other. Experiments on two datasets show that the proposed model significantly outperforms strong baselines in both one-shot and five-shot settings.

Moreover, this book assist in developing skills pertaining to R programming, data wrangling with dplyr, data visualization with ggplot2 and algorithm building with caret amongst others.

Regression is a modeling task that involves predicting a numeric value given an input. Linear regression is the standard algorithm for regression that assumes a linear relationship between inputs and the target variable. An extension to linear regression invokes adding penalties to the loss function during training that encourages simpler models that have smaller coefficient values. These extensions are referred to as regularized linear regression or penalized linear regression. Ridge Regression is a popular type of regularized linear regression that includes an L2 penalty.

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