The phenomenon of benign overfitting, where a predictor perfectly fits noisy training data while attaining low expected loss, has received much attention in recent years, but still remains not fully understood beyond simple linear regression setups. In this paper, we show that for regression, benign overfitting is ``biased'' towards certain types of problems, in the sense that its existence on one learning problem precludes its existence on other learning problems. On the negative side, we use this to argue that one should not expect benign overfitting to occur in general, for several natural extensions of the plain linear regression problems studied so far. We then turn to classification problems, and show that the situation there is much more favorable. Specifically, we consider a model where an arbitrary input distribution of some fixed dimension $k$ is concatenated with a high-dimensional distribution, and prove that the max-margin predictor (to which gradient-based methods are known to converge in direction) is asymptotically biased towards minimizing the expected \emph{squared hinge loss} w.r.t. the $k$-dimensional distribution. This allows us to reduce the question of benign overfitting in classification to the simpler question of whether this loss is a good surrogate for the misclassification error, and use it to show benign overfitting in some new settings.

This article was published as a part of the Data Science Blogathon. Will tomorrow be a sunny day? What are the chances that a student will get into that dream university? These and many more real-world "decision" scenarios need a standard mechanism. Step in Logistic Regression may be stated very simply as an estimation of the probability of an event occurring. In the next few minutes, we shall understand Logistic Regression from A-to-Z.

Convolutional Neural Networks (CNNs) are artificial learning systems typically based on two operations: convolution, which implements feature extraction through filtering, and pooling, which implements dimensionality reduction. The impact of pooling in the classification performance of the CNNs has been highlighted in several previous works, and a variety of alternative pooling operators have been proposed. However, only a few of them tackle with the uncertainty that is naturally propagated from the input layer to the feature maps of the hidden layers through convolutions. In this paper we present a novel pooling operation based on (type-1) fuzzy sets to cope with the local imprecision of the feature maps, and we investigate its performance in the context of image classification. Fuzzy pooling is performed by fuzzification, aggregation and defuzzification of feature map neighborhoods. It is used for the construction of a fuzzy pooling layer that can be applied as a drop-in replacement of the current, crisp, pooling layers of CNN architectures. Several experiments using publicly available datasets show that the proposed approach can enhance the classification performance of a CNN. A comparative evaluation shows that it outperforms state-of-the-art pooling approaches.

Development of new algorithms in the area of machine learning, especially clustering, comparative studies of such algorithms as well as testing according to software engineering principles requires availability of labeled data sets. While standard benchmarks are made available, a broader range of such data sets is necessary in order to avoid the problem of overfitting. In this context, theoretical works on axiomatization of clustering algorithms, especially axioms on clustering preserving transformations are quite a cheap way to produce labeled data sets from existing ones. However, the frequently cited axiomatic system of Kleinberg:2002, as we show in this paper, is not applicable for finite dimensional Euclidean spaces, in which many algorithms like $k$-means, operate. In particular, the so-called outer-consistency axiom fails upon making small changes in datapoint positions and inner-consistency axiom is valid only for identity transformation in general settings. Hence we propose an alternative axiomatic system, in which Kleinberg's inner consistency axiom is replaced by a centric consistency axiom and outer consistency axiom is replaced by motion consistency axiom. We demonstrate that the new system is satisfiable for a hierarchical version of $k$-means with auto-adjusted $k$, hence it is not contradictory. Additionally, as $k$-means creates convex clusters only, we demonstrate that it is possible to create a version detecting concave clusters and still the axiomatic system can be satisfied. The practical application area of such an axiomatic system may be the generation of new labeled test data from existent ones for clustering algorithm testing. %We propose the gravitational consistency as a replacement which does not have this deficiency.

Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing DeepPAMM, a versatile deep learning framework that is well-founded from a statistical point of view, yet with enough flexibility for modeling complex hazard structures. We illustrate that DeepPAMM is competitive with other machine learning approaches with respect to predictive performance while maintaining interpretability through benchmark experiments and an extended case study.

Benign overfitting demonstrates that overparameterized models can perform well on test data while fitting noisy training data. However, it only considers the final min-norm solution in linear regression, which ignores the algorithm information and the corresponding training procedure. In this paper, we generalize the idea of benign overfitting to the whole training trajectory instead of the min-norm solution and derive a time-variant bound based on the trajectory analysis. Starting from the time-variant bound, we further derive a time interval that suffices to guarantee a consistent generalization error for a given feature covariance. Unlike existing approaches, the newly proposed generalization bound is characterized by a time-variant effective dimension of feature covariance. By introducing the time factor, we relax the strict assumption on the feature covariance matrix required in previous benign overfitting under the regimes of overparameterized linear regression with gradient descent. This paper extends the scope of benign overfitting, and experiment results indicate that the proposed bound accords better with empirical evidence.

There are lots of different approaches to managing your own code, which will differ depending on your requirements, personality, technical know-how, role, and numerous other factors. While a highly-experienced developer may have an incredibly regimented method of organizing their code across multiple languages, projects, and use cases, a data analyst that rarely writes their own code may be much more ad hoc and lackadaisical out of lack of necessity. There really is no right or wrong, it's simply a matter of what works -- and is appropriate -- for you. To be specific, what I'm referring to by "managing code" is how you organize, store, and recall different pieces of code you, yourself, have written and found useful as long-term additions to your programming toolbox. Programming is all about automating, and so if, as someone who writes code, you find that you are performing similar tasks repetitively, it's only makes sense that you somehow automated the recalling of the code associated with that task.

I hope you are all safe and healthy. It's also been a while since I've gotten my hands dirty in writing scripts and analyzing data. So, I'll start with something kinda light for me -- analyzing one of the go-to datasets for projects and demos, the Boston housing dataset. The Boston housing dataset contains information collected by the U.S Census Service concerning housing in the area of Boston Massachusetts. It has 506 samples and 14 variables.

The Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research (AWI) is a member of the Helmholtz Association (HGF) and funded by federal and state government. AWI focuses on polar and marine research in a variety of disciplines such as biology, oceanography, geology, geochemistry and geophysics thus allowing multidisciplinary approaches to scientific goals. Background Climate models are essential for understanding complex physical and biogeochemical interactions across the planet. However, these models rely on many parameters that are necessary to accurately describe the effects of small-scale structures and processes that cannot be directly simulated. The project's goal is to develop data-driven methods of accurate, efficient parameter estimation in climate models.

Though we're living through a time of extraordinary innovation in GPU-accelerated machine learning, the latest research papers frequently (and prominently) feature algorithms that are decades, in certain cases 70 years old. Some might contend that many of these older methods fall into the camp of'statistical analysis' rather than machine learning, and prefer to date the advent of the sector back only so far as 1957, with the invention of the Perceptron. Given the extent to which these older algorithms support and are enmeshed in the latest trends and headline-grabbing developments in machine learning, it's a contestable stance. So let's take a look at some of the'classic' building blocks underpinning the latest innovations, as well as some newer entries that are making an early bid for the AI hall of fame. In 2017 Google Research led a research collaboration culminating in the paper Attention Is All You Need.