Clustering is sometimes called "unsupervised classification", a term that I have mixed feelings on for reasons I will cover shortly, but it provides a good enough explanation of the problem to be worth covering. First, the problem is unsupervised -- we won't have a labeled dataset to guide our logic. Secondly we are looking to separate items into classes based on the predictors (technically they are not predictors they are "features" here because there is no response). The difference is that in supervised classification the class structure is known and labeled, whereas in clustering we are inventing the class structure from the feature values alone. In supervised classification we used the labels to single out one class and looked for predictors that had two qualities: 1) They had fairly common values for every example of that class and 2) they separated that class from others.

Choosing the right metric is crucial while evaluating machine learning (ML) models. Various metrics are proposed to evaluate ML models in different applications, and I thought it may be helpful to provide a summary of popular metrics in a here, for better understanding of each metric and the applications they can be used for. In some applications looking at a single metric may not give you the whole picture of the problem you are solving, and you may want to use a subset of the metrics discussed in this post to have a concrete evaluation of your models. Here, I provide a summary of 20 metrics used for evaluating machine learning models. There is no need to mention that there are various other metrics used in some applications (FDR, FOR, hit@k, etc.), which I am skipping here.

Jupyter notebooks that walk you through the fundamentals of Machine Learning and Deep Learning in Python using Scikit-Learn, Keras and TensorFlow 2. You can access this material here. For other free tutorials (including from Berkeley, Harvard, Columbia, Google, Microsoft and so on), follow this link.

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.

This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for solving this computational statistics problem under the following assumptions: 1) neither the prior model nor the likelihood function are Gaussian and neither can be approximated by a Gaussian measure; 2) the number of functional input (system parameters) and functional output (quantity of interest) can be large; 3) the number of available realizations of the prior model is small, leading to the small-data challenge typically associated with expensive numerical simulations; the number of experimental realizations is also small; 4) the number of the posterior realizations required for decision is much larger than the available initial dataset. The method and its mathematical aspects are detailed. Three applications are presented for validation: The first two involve mathematical constructions aimed to develop intuition around the method and to explore its performance. The third example aims to demonstrate the operational value of the method using a more complex application related to the statistical inverse identification of the non-Gaussian matrix-valued random elasticity field of a damaged biological tissue (osteoporosis in a cortical bone) using ultrasonic waves.

Noname manuscript No. (will be inserted by the editor)ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels Angus Dempster · Fran cois Petitjean· Geoffrey I. Webb Received: date / Accepted: date Abstract Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many existing methods focus on a single type of feature such as shape or frequency. Building on the recent success of convolutional neural networks for time series classification, we show that simple linear classifiers using random convolutional kernels achieve state-of-the-art accuracy with a fraction of the computational expense of existing methods. Keywords scalable · time series classification · random · convolution 1 Introduction Most methods for time series classification that attain state-of-the-art ...

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and non-linear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.

Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the Hessian and Fisher information matrix, to incorporate geometric information into SVGD updates. We achieve this by presenting a generalization of SVGD that replaces the scalar-valued kernels in vanilla SVGD with more general matrix-valued kernels. This yields a significant extension of SVGD, and more importantly, allows us to flexibly incorporate various preconditioning matrices to accelerate the exploration in the probability landscape. Empirical results show that our method outperforms vanilla SVGD and a variety of baseline approaches over a range of real-world Bayesian inference tasks.

Knowledge Graphs (KGs) are composed of structured information about a particular domain in the form of entities and relations. In addition to the structured information KGs help in facilitating interconnectivity and interoperability between different resources represented in the Linked Data Cloud. KGs have been used in a variety of applications such as entity linking, question answering, recommender systems, etc. However, KG applications suffer from high computational and storage costs. Hence, there arises the necessity for a representation able to map the high dimensional KGs into low dimensional spaces, i.e., embedding space, preserving structural as well as relational information. This paper conducts a survey of KG embedding models which not only consider the structured information contained in the form of entities and relations in a KG but also the unstructured information represented as literals such as text, numerical values, images, etc. Along with a theoretical analysis and comparison of the methods proposed so far for generating KG embeddings with literals, an empirical evaluation of the different methods under identical settings has been performed for the general task of link prediction.

The traditional offline approaches are no longer sufficient for building modern recommender systems in domains such as online news services, mainly due to the high dynamics of environment changes and necessity to operate on a large scale with high data sparsity. The ability to balance exploration with exploitation makes the multi-armed bandits an efficient alternative to the conventional methods, and a robust user segmentation plays a crucial role in providing the context for such online recommendation algorithms. In this work, we present an unsupervised and trend-responsive method for segmenting users according to their semantic interests, which has been integrated with a real-world system for large-scale news recommendations. The results of an online A/B test show significant improvements compared to a global-optimization algorithm on several services with different characteristics. Based on the experimental results as well as the exploration of segments descriptions and trend dynamics, we propose extensions to this approach that address particular real-world challenges for different use-cases. Moreover, we describe a method of generating traceable publishing insights facilitating the creation of content that serves the diversity of all users needs.