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.

As part of my Data Science class with General Assembly, we each gave a presentation about a real-world application of data science. My talk was about using machine learning to detect fraud on Skype, and was based upon an excellent paper by Microsoft Research published in November 2013. Although Skype already had measures in place to detect fraud (e.g., credit card fraud, spam instant messages), the research team's goal was to improve the detection of "stealthy fraudulent users" that evade Skype's defenses for a prolonged period. They built a machine learning classifier that flagged potentially fraudulent users, and was able to detect 68% of these users with a false positive rate of 5%. The novelty in their approach was the fusing of disparate data types (profile information, Skype product usage, and Skype social activity) into a single classifier.

It was supposed to be the perfect main event Dana White originally envisioned for UFC 200, but light heavyweight champion Daniel Cormier's impromptu square off with the legendary Anderson Silva still has all the fixings of a major mixed martial arts showdown. Originally, Cormier was to rematch Jon Jones in a unification bout Saturday night at Las Vegas' T-Mobile Arena. However, earlier this week it was revealed Jones failed a drug test and was pulled from the main event in lieu of an investigation into whether or not he used performance enhancing drugs. Silva, who last fought in February but hasn't claimed a victory since 2012, stepped up and essentially saved what was intended to be UFC's biggest PPV event since 100th edition seven years ago. Still, the bout was bumped down two slots with women's bantam weight champion Miesha Tate's face off with challenger Amanda Nunes leapfrogging, and Brock Lesnar and Mark Hunt's battle standing as the main event.

This is the third in a series of posts on how to build a Data Science Portfolio. If you like this and want to know when the next post in the series is released, you can subscribe at the bottom of the page. Data science companies are increasingly looking at portfolios when making hiring decisions. One of the reasons for this is that a portfolio is the best way to judge someone's real-world skills. The good news for you is that a portfolio is entirely within your control. If you put some work in, you can make a great portfolio that companies are impressed by. The first step in making a high-quality portfolio is to know what skills to demonstrate. Any good portfolio will be composed of multiple projects, each of which may demonstrate 1-2 of the above points. This is the third post in a series that will cover how to make a well-rounded data science portfolio.

Machine Learning is a subfield within Artificial Intelligence that builds algorithms that allow computers to learn to perform tasks from data instead of being explicitly programmed. We can make machines learn to do things! The first time I heard that, it blew my mind. That means that we can program computers to learn things by themselves! The ability of learning is one of the most important aspects of intelligence. Translating that power to machines, sounds like a huge step towards making them more intelligent. And in fact, Machine Learning is the area that is making most of the progress in Artificial Intelligence today; being a trendy topic right now and pushing the possibility to have more intelligent machines.

We investigate a long-debated question, which is how to create predictive models of recidivism that are sufficiently accurate, transparent, and interpretable to use for decision-making. This question is complicated as these models are used to support different decisions, from sentencing, to determining release on probation, to allocating preventative social services. Each use case might have an objective other than classification accuracy, such as a desired true positive rate (TPR) or false positive rate (FPR). Each (TPR, FPR) pair is a point on the receiver operator characteristic (ROC) curve. We use popular machine learning methods to create models along the full ROC curve on a wide range of recidivism prediction problems. We show that many methods (SVM, Ridge Regression) produce equally accurate models along the full ROC curve. However, methods that designed for interpretability (CART, C5.0) cannot be tuned to produce models that are accurate and/or interpretable. To handle this shortcoming, we use a new method known as SLIM (Supersparse Linear Integer Models) to produce accurate, transparent, and interpretable models along the full ROC curve. These models can be used for decision-making for many different use cases, since they are just as accurate as the most powerful black-box machine learning models, but completely transparent, and highly interpretable.

When sufficient labeled data are available, classical criteria based on Receiver Operating Characteristic (ROC) or Precision-Recall (PR) curves can be used to compare the performance of un-supervised anomaly detection algorithms. However , in many situations, few or no data are labeled. This calls for alternative criteria one can compute on non-labeled data. In this paper, two criteria that do not require labels are empirically shown to discriminate accurately (w.r.t. ROC or PR based criteria) between algorithms. These criteria are based on existing Excess-Mass (EM) and Mass-Volume (MV) curves, which generally cannot be well estimated in large dimension. A methodology based on feature sub-sampling and aggregating is also described and tested, extending the use of these criteria to high-dimensional datasets and solving major drawbacks inherent to standard EM and MV curves.

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Although ensembles of nested dichotomies with random structure have been shown to perform well in practice, using a more sophisticated class subset selection method can be used to improve classification accuracy. We investigate an approach to this problem called random-pair selection, and evaluate its effectiveness compared to other published methods of subset selection. We show that our method outperforms other methods in many cases when forming ensembles of nested dichotomies, and is at least on par in all other cases.

We study the residual bootstrap (RB) method in the context of high-dimensional linear regression. Specifically, we analyze the distributional approximation of linear contrasts $c^{\top} (\hat{\beta}_{\rho}-\beta)$, where $\hat{\beta}_{\rho}$ is a ridge-regression estimator. When regression coefficients are estimated via least squares, classical results show that RB consistently approximates the laws of contrasts, provided that $p\ll n$, where the design matrix is of size $n\times p$. Up to now, relatively little work has considered how additional structure in the linear model may extend the validity of RB to the setting where $p/n\asymp 1$. In this setting, we propose a version of RB that resamples residuals obtained from ridge regression. Our main structural assumption on the design matrix is that it is nearly low rank --- in the sense that its singular values decay according to a power-law profile. Under a few extra technical assumptions, we derive a simple criterion for ensuring that RB consistently approximates the law of a given contrast. We then specialize this result to study confidence intervals for mean response values $X_i^{\top} \beta$, where $X_i^{\top}$ is the $i$th row of the design. More precisely, we show that conditionally on a Gaussian design with near low-rank structure, RB simultaneously approximates all of the laws $X_i^{\top}(\hat{\beta}_{\rho}-\beta)$, $i=1,\dots,n$. This result is also notable as it imposes no sparsity assumptions on $\beta$. Furthermore, since our consistency results are formulated in terms of the Mallows (Kantorovich) metric, the existence of a limiting distribution is not required.

We propose a novel methodology, forest floor, to visualize and interpret random forest (RF) models. RF is a popular and useful tool for non-linear multi-variate classification and regression, which yields a good trade-off between robustness (low variance) and adaptiveness (low bias). Direct interpretation of a RF model is difficult, as the explicit ensemble model of hundreds of deep trees is complex. Nonetheless, it is possible to visualize a RF model fit by its mapping from feature space to prediction space. Hereby the user is first presented with the overall geometrical shape of the model structure, and when needed one can zoom in on local details. Dimensional reduction by projection is used to visualize high dimensional shapes. The traditional method to visualize RF model structure, partial dependence plots, achieve this by averaging multiple parallel projections. We suggest to first use feature contributions, a method to decompose trees by splitting features, and then subsequently perform projections. The advantages of forest floor over partial dependence plots is that interactions are not masked by averaging. As a consequence, it is possible to locate interactions, which are not visualized in a given projection. Furthermore, we introduce: a goodness-of-visualization measure, use of colour gradients to identify interactions and an out-of-bag cross validated variant of feature contributions.