A few weeks ago I came across with an interesting article titled "A Music Taste Analysis Using Spotify API and Python". In this article, an author tries to analyze not only his but also a fiancée's preference to determine what the data has to say about this. Thus, he compares two different profiles in terms of music features, which are provided by Spotify's API, simultaneously. While reading it, I was curious to not only analyze my own preference but also to play with my Spotify data. Therefore, I wanted to cluster my saved songs on Spotify into separate playlists that would represent a specific mood I have while listening to them. Initially, it is worth mentioning that likewise Twitter, Slack, and Facebook Spotify offers an API for developers to explore their music database and get insights into our listening habits.

Data Science is such a broad field that includes several subdivisions like data preparation and exploration, data representation and transformation, data visualization and presentation, predictive analytics, and machine learning, etc. For beginners, it's only natural to raise the following question: What skills do I need to become a data scientist? This article will discuss 10 essential skills that are necessary for practicing data scientists. These skills could be grouped into 2 categories, namely, technological skills (Math & Statistics, Coding Skills, Data Wrangling & Preprocessing Skills, Data Visualization Skills, Machine Learning Skills, and Real World Project Skills) and soft skills (Communication Skills, Lifelong Learning Skills, Team Player Skills, and Ethical Skills). Data science is a field that is ever-evolving, however mastering the foundations of data science will provide you with the necessary background that you need to pursue advanced concepts such as deep learning, artificial intelligence, etc.

Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo sampling method. One drawback is that it requires the computation of the full gradient at each iteration, an expensive operation if the dimension of the problem is high. We propose a new sampling method: Random Coordinate LMC (RC-LMC). At each iteration, a single coordinate is randomly selected to be updated by a multiple of the partial derivative along this direction plus noise, and all other coordinates remain untouched. We investigate the total complexity of RC-LMC and compare it with the classical LMC for log-concave probability distributions. When the gradient of the log-density is Lipschitz, RC-LMC is less expensive than the classical LMC if the log-density is highly skewed for high dimensional problems, and when both the gradient and the Hessian of the log-density are Lipschitz, RC-LMC is always cheaper than the classical LMC, by a factor proportional to the square root of the problem dimension. In the latter case, our estimate of complexity is sharp with respect to the dimension.

The Heavy Ball Method (Polyak, 1964), proposed by Polyak over five decades ago, is a first-order method for optimizing continuous functions. While its stochastic counterpart has proven extremely popular in training deep networks, there are almost no known functions where deterministic Heavy Ball is provably faster than the simple and classical gradient descent algorithm in non-convex optimization. The success of Heavy Ball has thus far eluded theoretical understanding. Our goal is to address this gap, and in the present work we identify two non-convex problems where we provably show that the Heavy Ball momentum helps the iterate to enter a benign region that contains a global optimal point faster. We show that Heavy Ball exhibits simple dynamics that clearly reveal the benefit of using a larger value of momentum parameter for the problems. The first of these optimization problems is the phase retrieval problem, which has useful applications in physical science. The second of these optimization problems is the cubic-regularized minimization, a critical subroutine required by Nesterov-Polyak cubic-regularized method (Nesterov & Polyak (2006)) to find second-order stationary points in general smooth non-convex problems. Poylak's Heavy Ball method (Polyak (1964)) has been very popular in modern non-convex optimization and deep learning, and the stochastic version (a.k.a. SGD with momentum) has become the de facto algorithm for training neural nets.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by the connection between geometry of the loss landscape and generalization---including a generalization bound that we prove here---we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-{10, 100}, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels.

Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear filters to design state-of-the-art neural network models. Here, we exploit tools from random matrix theory to make precise statements about how the eigenspectrum of a matrix changes under such nonlinear transformations. In particular, we show that very little change occurs in the informative eigenstructure even under drastic sparsification/quantization, and consequently that very little downstream performance loss occurs with very aggressively sparsified or quantized spectral clustering. We illustrate how these results depend on the nonlinearity, we characterize a phase transition beyond which spectral clustering becomes possible, and we show when such nonlinear transformations can introduce spurious non-informative eigenvectors.

However, the advantage of using convolutional networks over fully-connected networks is not understood from a theoretical perspective. In this work, we show how convolutional networks can leverage locality in the data, and thus achieve a computational advantage over fully-connected networks. Specifically, we show a class of problems that can be efficiently solved using convolutional networks trained with gradient-descent, but at the same time is hard to learn using a polynomial-size fully-connected network. Convolutional neural networks (LeCun et al., 1998; Krizhevsky et al., 2012) achieve state-of-the-art performance on every possible task in computer vision. However, while the empirical success of convolutional networks is indisputable, the advantage of using them is not well understood from a theoretical perspective.

The t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm is a ubiquitously employed dimensionality reduction (DR) method. Its non-parametric nature and impressive efficacy motivated its parametric extension. It is however bounded to a user-defined perplexity parameter, restricting its DR quality compared to recently developed multi-scale perplexity-free approaches. This paper hence proposes a multi-scale parametric t-SNE scheme, relieved from the perplexity tuning and with a deep neural network implementing the mapping. It produces reliable embeddings with out-of-sample extensions, competitive with the best perplexity adjustments in terms of neighborhood preservation on multiple data sets.

The Gaussian mixture model (GMM) provides a convenient yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as convenient as the classical GMM, but can generate a more informative evidential partition for the considered dataset. Experiments with synthetic and real datasets demonstrate the good performance of the proposed method as compared with some other prototype-based and model-based clustering techniques.

Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank approaches are unable to mine complex, interleaved features that underlie hierarchical semantics. Recently, deep matrix factorization (deep MF) was introduced to deal with the extraction of several layers of features and has been shown to reach outstanding performances on unsupervised tasks. Deep MF was motivated by the success of deep learning, as it is conceptually close to some neural networks paradigms. In this paper, we present the main models, algorithms, and applications of deep MF through a comprehensive literature review. We also discuss theoretical questions and perspectives of research.