Unsupervised machine learning is the machine learning task of inferring a function to describe hidden structure from "unlabeled" data (a classification or categorization is not included in the observations). While there is an exhaustive list of clustering algorithms available (whether you use R or Python's Scikit-Learn), I will attempt to cover the basic concepts. The most common and simplest clustering algorithm out there is the K-Means clustering. This algorithms involve you telling the algorithms how many possible cluster (or K) there are in the dataset. The algorithm then iteratively moves the k-centers and selects the datapoints that are closest to that centroid in the cluster.

Tree boosting has empirically proven to be efficient for predictive mining for both classification and regression. For many years, MART (multiple additive regression trees) has been the tree boosting method of choice. But a starting from 2015, a first to try, always winning algorithm surged to the surface: XGBoost. This algorithm re-implements the tree boosting and gained popularity by winning Kaggle and other data science competition. In the thesis Tree Boosting With XGBoost – Why Does XGBoost Win "Every" Machine Learning Competition, the author Didrik Nielsen from Norwegian University of Science and Technology is trying to: The paper introduce in first place the supervised learning task and discuss the model selection techniques.

The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient estimator. This generalizes recent work on using Determinantal Point Processes (DPPs) for mini-batch diversification (Zhang et al., 2017) to the broader class of repulsive point processes. We first show that the phenomenon of variance reduction by diversified sampling generalizes in particular to non-stationary point processes. We then show that other point processes may be computationally much more efficient than DPPs. In particular, we propose and investigate Poisson Disk sampling---frequently encountered in the computer graphics community---for this task. We show empirically that our approach improves over standard SGD both in terms of convergence speed as well as final model performance.

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb p(Y = m | X = x) = \theta_m(x)$, $1 \leq m \leq M$, and $\theta_1(x), \dots, \theta_M(x)$ are unknown Lipschitz functions. Given a test point $X$, our goal is to estimate $\theta_1(X), \dots, \theta_M(X)$. An approach based on nonparametric smoothing uses a localization technique, i.e. the weight of observation $(X_i, Y_i)$ depends on the distance between $X_i$ and $X$. However, local estimates strongly depend on localizing scheme. In our solution we fix several schemes $W_1, \dots, W_K$, compute corresponding local estimates $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$ for each of them and apply an aggregation procedure. We propose an algorithm, which constructs a convex combination of the estimates $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$ such that the aggregated estimate behaves approximately as well as the best one from the collection $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$. We also study theoretical properties of the procedure, prove oracle results and establish rates of convergence under mild assumptions.

Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle the sizes of modern high-dimensional data sets (often on the order of terabytes), and assume Gaussian samples. To address these deficiencies, we introduce HP-CONCORD, a highly scalable optimization method for estimating a sparse inverse covariance matrix based on a regularized pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal gradient method uses a novel communication-avoiding linear algebra algorithm and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving parallel scalability on problems with up to ~819 billion parameters (1.28 million dimensions); even on a single node, HP-CONCORD demonstrates scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to estimate the underlying dependency structure of the brain from fMRI data, and use the result to identify functional regions automatically. The results show good agreement with a clustering from the neuroscience literature.

The appeal of metric evaluation of research impact has attracted considerable interest in recent times. Although the public at large and administrative bodies are much interested in the idea, scientists and other researchers are much more cautious, insisting that metrics are but an auxiliary instrument to the qualitative peer-based judgement. The goal of this article is to propose availing of such a well positioned construct as domain taxonomy as a tool for directly assessing the scope and quality of research. We first show how taxonomies can be used to analyse the scope and perspectives of a set of research projects or papers. Then we proceed to define a research team or researcher's rank by those nodes in the hierarchy that have been created or significantly transformed by the results of the researcher. An experimental test of the approach in the data analysis domain is described. Although the concept of taxonomy seems rather simplistic to describe all the richness of a research domain, its changes and use can be made transparent and subject to open discussions.

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$, as long as $Y$ is also a regressor. On the contrary, if $P(X \mid Y, Z) \neq P(X \mid Y)$, $Z$ might improve prediction results. FIT applies to thousand-dimensional random variables with a hundred thousand samples in a fraction of the time required by alternative methods. We provide an extensive evaluation that compares FIT to six extant nonparametric independence tests. The evaluation shows that FIT has low probability of making both Type I and Type II errors compared to other tests, especially as the number of available samples grows. Our implementation of FIT is publicly available.

Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes that data comes from a mixture of a number of Gaussians as well as a uniform "background" component assumed to contain outliers and other non-interesting observations. We develop a novel method based on robust loss minimization that performs well in clustering such GMM with a uniform background. We give theoretical guarantees for our clustering algorithm to obtain best clustering results with high probability. Besides, we show that the result of our algorithm does not depend on initialization or local optima, and the parameter tuning is an easy task. By numeric simulations, we demonstrate that our algorithm enjoys high accuracy and achieves the best clustering results given a large enough sample size.

I recently participated in this Kaggle competition (WIDS Datathon by Stanford) where I was able to land up in Top 10 using various boosting algorithms. Since then, I have been very curious about the fine workings of each model including parameter tuning, pros and cons and hence decided to write this blog. Despite the recent re-emergence and popularity of neural networks, I am focusing on boosting algorithms because they are still more useful in the regime of limited training data, little training time and little expertise for parameter tuning. Since XGBoost (often called GBM Killer) has been in the machine learning world for a longer time now with lots of articles dedicated to it, this post will focus more on CatBoost & LGBM. LightGBM uses a novel technique of Gradient-based One-Side Sampling (GOSS) to filter out the data instances for finding a split value while XGBoost uses pre-sorted algorithm & Histogram-based algorithm for computing the best split.

Data Science is quite a large and diverse field. As a result, it is really difficult to be a jack of all trades. Traditionally, Data Science would focus on mathematics, computer science and domain expertise. While I will briefly cover some computer science fundamentals, the bulk of this blog will mostly cover the mathematical basics one might either need to brush up on (or even take an entire course). In most data science workplaces, software skills are a must. While I understand most of you reading this are more math heavy by nature, realize the bulk of data science (dare I say 80%) is collecting, cleaning and processing data into a useful form.