Naive Bayes Nearest Neighbour (NBNN) is a simple and effective framework which addresses many of the pitfalls of K-Nearest Neighbour (KNN) classification. It has yielded competitive results on several computer vision benchmarks. Its central tenet is that during NN search, a query is not compared to every example in a database, ignoring class information. Instead, NN searches are performed within each class, generating a score per class. A key problem with NN techniques, including NBNN, is that they fail when the data representation does not capture perceptual (e.g.~class-based) similarity. NBNN circumvents this by using independent engineered descriptors (e.g.~SIFT). To extend its applicability outside of image-based domains, we propose to learn a metric which captures perceptual similarity. Similar to how Neighbourhood Components Analysis optimizes a differentiable form of KNN classification, we propose "Class Conditional" metric learning (CCML), which optimizes a soft form of the NBNN selection rule. Typical metric learning algorithms learn either a global or local metric. However, our proposed method can be adjusted to a particular level of locality by tuning a single parameter. An empirical evaluation on classification and retrieval tasks demonstrates that our proposed method clearly outperforms existing learned distance metrics across a variety of image and non-image datasets.

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful representation of this homological information is a persistence diagram (PD). Efforts have been made to map PDs into spaces with additional structure valuable to machine learning tasks. We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs. The discriminatory power of PIs is compared against existing methods, showing significant performance gains. We explore the use of PIs with vector-based machine learning tools, such as linear sparse support vector machines, which identify features containing discriminating topological information. Finally, high accuracy inference of parameter values from the dynamic output of a discrete dynamical system (the linked twist map) and a partial differential equation (the anisotropic Kuramoto-Sivashinsky equation) provide a novel application of the discriminatory power of PIs.

Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR. We propose an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters predefined groups of entities, a metaheuristic genetic algorithm with adapted Lloyd's algorithm for K-means clustering, a two-stage approach, and a modified algorithm of Sp{\"a}th \cite{Spath1979} for solving generalized CLR. We examine the performance of our algorithms on a stock keeping unit (SKU) clustering problem employed in forecasting halo and cannibalization effects in promotions using real-world retail data from a large supermarket chain. In the SKU clustering problem, the retailer needs to cluster SKUs based on their seasonal effects in response to promotions. The seasonal effects are the results of regressions with predictors being promotion mechanisms and seasonal dummies performed over clusters generated. We compare the performance of all proposed algorithms for the SKU problem with real-world and synthetic data.

The early identification of toxic paraquat (PQ) poisoning in patients critical to ensure timely and accurate prognosis. Though plasma PQ concentration has been reported as a clinical indicator of PQ poisoning, it is not commonly applied in practice due to the inconvenient necessary instruments and operation. In this study, we explored the use of blood routine indexes to identify the degree of PQ toxicity and/or diagnose PQ poisoning in patients via machine learning approach. Specifically, we developed a method based on support vector machine combined with the feature selection technique to accurately predict PQ poisoning risk status, then tested the method on 79 (42 male and 37 female; 41 living and 38 deceased) patients. The detection method was rigorously evaluated against a real-world dataset to determine its accuracy, sensitivity and specificity. Feature selection was also applied to identify factors correlated with risk status, and results showed that there are significant differences in blood routine indexes between dead and living PQ-poisoned individuals (p-value 0.01).

Celestion loudspeakers have powered the performances of many noted guitar and bass players, including legends such as Jimi Hendrix. Deciding whether a loudspeaker is good enough for professional musicians is a lengthy and painstaking process. Each speaker has its own unique sound based on a combination of sonic characteristics, such as midrange character and brightness. Evaluating a musical instrument loudspeaker involves subjective judgement about whether it generates a "good" sound. Only engineers with years of experience can reliably make that decision, and then only after repeated listening to a single loudspeaker and comparing the sounds it produces with those produced by a reference speaker.

We study classification problems where features are corrupted by noise and where the magnitude of the noise in each feature is influenced by the resources allocated to its acquisition. This is the case, for example, when multiple sensors share a common resource (power, bandwidth, attention, etc.). We develop a method for computing the optimal resource allocation for a variety of scenarios and derive theoretical bounds concerning the benefit that may arise by non-uniform allocation. We further demonstrate the effectiveness of the developed method in simulations.

Activists Cheer On EU's'Right To An Explanation' For Algorithmic Decisions, But How Will It Work When There's Nothing To Explain? I saw a lot of excitement and happiness a week or so ago around some reports that the EU's new General Data Protection Regulations (GDPR) might possibly include a "right to an explanation" for algorithmic decisions. It's not clear if this is absolutely true, but it's based on a reading of the agreed upon text of the GDPR, which is scheduled to go into effect in two years. Slated to take effect as law across the EU in 2018, it will restrict automated individual decision-making (that is, algorithms that make decisions based on user-level predictors) which "significantly affect" users. The law will also create a "right to explanation," whereby a user can ask for an explanation of an algorithmic decision that was made about them.

Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric non-linear regression models and better interpretability and scalability than the non-parametric regression models. However, achieving sparsity simultaneously in the number of nonparametric components as well as in the variables within each nonparametric component poses a stiff computational challenge. In this article, we develop a novel Bayesian additive regression model using a combination of hard and soft shrinkages to separately control the number of additive components and the variables within each component. An efficient algorithm is developed to select the importance variables and estimate the interaction network. Excellent performance is obtained in simulated and real data examples.

Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a Bayesian quantile additive regression trees model that shows very good predictive performance illustrated using simulation studies and real data applications. Further extension to tackle binary classification problems is also considered.