Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used to define a distance between probability measures, known as the maximum mean discrepancy (MMD). A well-known advantage of mean embeddings and MMD is their low computational cost and low sample complexity. However, kernel mean embeddings have had limited applications to problems that consist in optimizing distributions, due to the difficulty of characterizing which Hilbert space vectors correspond to a probability distribution. In this note, we propose to leverage the kernel sums-of-squares parameterization of positive functions of Marteau-Ferey et al. [2020] to fit distributions in the MMD geometry. First, we show that when the kernel is characteristic, distributions with a kernel sum-of-squares density are dense. Then, we provide algorithms to optimize such distributions in the finite-sample setting, which we illustrate in a density fitting numerical experiment.

K-Nearest Neighbor (kNN)-based deep learning methods have been applied to many applications due to their simplicity and geometric interpretability. However, the robustness of kNN-based classification models has not been thoroughly explored and kNN attack strategies are underdeveloped. In this paper, we propose an Adversarial Soft kNN (ASK) loss to both design more effective kNN attack strategies and to develop better defenses against them. Our ASK loss approach has two advantages. First, ASK loss can better approximate the kNN's probability of classification error than objectives proposed in previous works. Second, the ASK loss is interpretable: it preserves the mutual information between the perturbed input and the kNN of the unperturbed input. We use the ASK loss to generate a novel attack method called the ASK-Attack (ASK-Atk), which shows superior attack efficiency and accuracy degradation relative to previous kNN attacks. Based on the ASK-Atk, we then derive an ASK-Defense (ASK-Def) method that optimizes the worst-case training loss induced by ASK-Atk.

Logistic Regression is a Supervised Learning algorithm, used for classification. It is used to predict probability of Target Variable. It produces results in binary format. It uses "Sigmoid Function" to give the outcomes. Just like the sigmoid curve, the outcomes can range from 0 to 1. Categorization is done on the basis of threshold value.

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal Component Analysis (PCA). Our proposed method can be used in high dimensional time series data which typically suffers from small sample size problem. Our method extracts a piece wise linear functional feature space and is particularly suitable for hard classification problems.The proposed framework converts time series data into functional data and uses classwise functional PCA for feature extraction followed by classification using a Bayesian linear classifier. We demonstrate the efficacy of our proposed method by applying it to both synthetic data sets and real time series data from diverse fields including but not limited to neuroscience, food science, medical sciences and chemometrics.

Processed data are insightful, and crude data are obtuse. A serious threat to data reliability is missing values. Such data leads to inaccurate analysis and wrong predictions. We propose an efficient technique to impute the missing value in the dataset based on correlation called FCMI (Feature Correlation based Missing Data Imputation). We have considered the correlation of the attributes of the dataset, and that is our central idea. Our proposed algorithm picks the highly correlated attributes of the dataset and uses these attributes to build a regression model whose parameters are optimized such that the correlation of the dataset is maintained. Experiments conducted on both classification and regression datasets show that the proposed imputation technique outperforms existing imputation algorithms.

Some of my most popular blogs on Medium are about libraries that I believe you should try. In this blog, I will focus on low-code machine learning libraries. The truth is that many data scientists believe that low-code libraries are shortcuts and should be avoided. I'm afraid I have to disagree! I think that low-code libraries should be included in our pipeline to help us make important decisions without wasting time.

Since the early 2000s, the amount of data collected has increased enormously due to the advent of internet giants such as Google, Netflix, Youtube, Amazon, Facebook, etc. Near to 2010, another "data wave" had come about when mobile phones became hugely popular. In 2020s, we anticipate another exponential rise in data when IoT devices become all-pervasive. Given this backdrop, building scalable systems becomes a sine qua non for machine learning solutions. Pre-2005, parallel processing libraries like MPI and PVM were popular for compute heavy tasks, based on which TensorFlow was designed later. Hence, the design was aimed to reduce data redundancy, by dividing larger tables into smaller tables, and link them using relationships (Normalization).

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that a single step size (learning rate) is used for all input variables. Extensions to gradient descent, like the Adaptive Movement Estimation (Adam) algorithm, use a separate step size for each input variable but may result in a step size that rapidly decreases to very small values. AdaMax is an extension to the Adam version of gradient descent that generalizes the approach to the infinite norm (max) and may result in a more effective optimization on some problems. In this tutorial, you will discover how to develop gradient descent optimization with AdaMax from scratch.

Population-based optimization algorithms, like evolutionary algorithms and swarm intelligence, often describe their dynamics in terms of the interplay between selective pressures and convergence. For example, strong selective pressures result in faster convergence and likely premature convergence. Weaker selective pressures may result in a slower convergence (greater computational cost) although perhaps locate a better or even global optima. An operator with a high selective pressure decreases diversity in the population more rapidly than operators with a low selective pressure, which may lead to premature convergence to suboptimal solutions. A high selective pressure limits the exploration abilities of the population.

As a review summarizing what has been done (up to 2017) already exists, it is advisable to start from there. The paper written by Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe and Seth Lloyd, focuses on quantum basic linear algebra subroutines (BLAS) -- as Fourier transforms, finding eigenvectors and eigenvalues, etc -- which are heavily used in machine learning algorithms, highlighting the advantages of using quantum rather than classical hardware. Indeed, the achievements are mainly in computational speed, although discussions on quantum support vector machine and quantum kernel appears. There is a very good introduction to quantum annealing and quantum Boltzman machine. An updated version (2018) is available on arXiv, although you cannot expect an over-comprehensive summary as the field of quantum computing is having a revolution each week. Nevertheless, the authors are among the pioneers thinking about the combination of both fields.