This post is on a project exploring an audio dataset in two dimensions. The results are hosted in a small web application on my university's servers -- have a play with it! Run the mouse over the purple dots to hear the sounds that are associated with the two-dimensional position vector. Feel free to play with the features used (MFCCs or Wavenet latent variables) and the method of dimensionality reduction (UMAP, t-SNE or PCA.) UMAP and t-SNE will also have parameters such as step amount or perplexity that can be tweaked. So what do we mean by dimensionality? It is an important topic in machine learning and data science that describes the potential complexity of a dataset. A dataset will comprise a multitude of data points, each having a constant amount of features, or dimensions.

The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not useful for classification. We show that, to the contrary, near state-of-the-art classification accuracy rates can be achieved when applying topological data analysis (TDA) to 3-dimensional point clouds of oriented minutiae points. We also apply TDA to fingerprint ink-roll images, which yields a lower accuracy rate but still shows promise, particularly since the only preprocessing is cropping; moreover, combining the two approaches outperforms each one individually. These methods use supervised learning applied to persistent homology and allow us to explore feature selection on barcodes, an important topic at the interface between TDA and machine learning. We test our classification algorithms on the NIST fingerprint database SD-27.

Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL divergence between a log-concave target density $f\left(\boldsymbol{\theta}\right)$ and its Laplace approximation $g\left(\boldsymbol{\theta}\right)$. The bound we present is computable: on the classical logistic regression model, we find our bound to be almost exact as long as the dimensionality of the parameter space is high. The approach we followed in this work can be extended to other Gaussian approximations, as we will do in an extended version of this work, to be submitted to the Annals of Statistics. It will then become a critical tool for characterizing whether, for a given problem, a given Gaussian approximation is suitable, or whether a more precise alternative method should be used instead.

We study platforms in the sharing economy and discuss the need for incentivizing users to explore options that otherwise would not be chosen. For instance, rental platforms such as Airbnb typically rely on customer reviews to provide users with relevant information about different options. Yet, often a large fraction of options does not have any reviews available. Such options are frequently neglected as viable choices, and in turn are unlikely to be evaluated, creating a vicious cycle. Platforms can engage users to deviate from their preferred choice by offering monetary incentives for choosing a different option instead. To efficiently learn the optimal incentives to offer, we consider structural information in user preferences and introduce a novel algorithm - Coordinated Online Learning (CoOL) - for learning with structural information modeled as convex constraints. We provide formal guarantees on the performance of our algorithm and test the viability of our approach in a user study with data of apartments on Airbnb. Our findings suggest that our approach is well-suited to learn appropriate incentives and increase exploration on the investigated platform.

In recent years, significant progress has been made in solving challenging problems across various domains using deep reinforcement learning (RL). Reproducing existing work and accurately judging the improvements offered by novel methods is vital to sustaining this progress. Unfortunately, reproducing results for state-of-the-art deep RL methods is seldom straightforward. In particular, non-determinism in standard benchmark environments, combined with variance intrinsic to the methods, can make reported results tough to interpret. Without significance metrics and tighter standardization of experimental reporting, it is difficult to determine whether improvements over the prior state-of-the-art are meaningful. In this paper, we investigate challenges posed by reproducibility, proper experimental techniques, and reporting procedures. We illustrate the variability in reported metrics and results when comparing against common baselines and suggest guidelines to make future results in deep RL more reproducible. We aim to spur discussion about how to ensure continued progress in the field by minimizing wasted effort stemming from results that are non-reproducible and easily misinterpreted.

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non-asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data.

KNN can easily be mapped to our real lives. If you want to learn about a person, of whom you have no information, you might like to find out about his close friends and the circles he moves in and gain access to his/her information!

If you were to ask me 2 most intuitive algorithms in machine learning – it would be k-Nearest Neighbours (kNN) and tree based algorithms. Both of them are simple to understand, easy to explain and perfect to demonstrate to people. Interestingly, we had skill tests for both these algorithms last month. If you are new to machine learning, make sure you test yourself on understanding of both of these algorithms. They are simplistic, but immensely powerful and used extensively in industry.

A modern aircraft may require on the order of thousands of custom shims to fill gaps between structural components in the airframe that arise due to manufacturing tolerances adding up across large structures. These shims are necessary to eliminate gaps, maintain structural performance, and minimize pull-down forces required to bring the aircraft into engineering nominal configuration for peak aerodynamic efficiency. Gap filling is a time-consuming process, involving either expensive by-hand inspection or computations on vast quantities of measurement data from increasingly sophisticated metrology equipment. Either case amounts to significant delays in production, with much of the time spent in the critical path of aircraft assembly. This work presents an alternative strategy for predictive shimming, based on machine learning and sparse sensing to first learn gap distributions from historical data, and then design optimized sparse sensing strategies to streamline data collection and processing. This new approach is based on the assumption that patterns exist in shim distributions across aircraft, which may be mined and used to reduce the burden of data collection and processing in future aircraft. Specifically, robust principal component analysis is used to extract low-dimensional patterns in the gap measurements while rejecting outliers. Next, optimized sparse sensors are obtained that are most informative about the dimensions of a new aircraft in these low-dimensional principal components. We demonstrate the success of the proposed approach, called PIXel Identification Despite Uncertainty in Sensor Technology (PIXI-DUST), on historical production data from 54 representative Boeing commercial aircraft. Our algorithm successfully predicts $99\%$ of shim gaps within the desired measurement tolerance using $3\%$ of the laser scan points typically required; all results are cross-validated.