Boosting is here to help. Boosting is a popular machine learning algorithm that increases accuracy of your model, something like when racers use nitrous boost to increase the speed of their car. Boosting uses a base machine learning algorithm to fit the data. This can be any algorithm, but Decision Tree is most widely used. For an answer to why so, just keep reading.

It was a striking story. "Machine Bias," the headline read, and the teaser proclaimed: "There's software used across the country to predict future criminals. And it's biased against blacks." ProPublica, a Pulitzer Prize–winning nonprofit news organization, had analyzed risk assessment software known as COMPAS. It is being used to forecast which criminals are most likely to reoffend.

One of the advantages that decision trees have over many other models is their ability to natively handle categorical predictors without having to first transform them (e.g., by using one-hot encoding). However, in this paper, we show how this capability can also lead to an inherent "absent levels" problem for decision tree based algorithms that, to the best of our knowledge, has never been thoroughly discussed, and whose consequences have never been carefully explored. This predicament occurs whenever there is indeterminacy in how to handle an observation that has reached a categorical split which was determined when the observation's level was absent during training. Although these incidents may appear to be innocuous, by using Leo Breiman and Adele Cutler's random forests FORTRAN code and the randomForest R package as motivating case studies, we show how overlooking the absent levels problem can systematically bias a model. Afterwards, we discuss some heuristics that can possibly be used to help mitigate the absent levels problem and, using three real data examples taken from public repositories, we demonstrate the superior performance and reliability of these heuristics over some of the existing approaches that are currently being employed in practice due to oversights in the software implementations of decision tree based algorithms. Given how extensively these algorithms have been used, it is conceivable that a sizable number of these models have been unknowingly and seriously affected by this issue---further emphasizing the need for the development of both theory and software that accounts for the absent levels problem.

While at Insight, I had the opportunity to consult on a data science project for AptDeco.com. AptDeco is a NYC based peer-to-peer online marketplace for buying and selling used furniture. The AptDeco team fills in any missing details about the furniture, creates high quality listings on their website, and even delivers the furniture when it's purchased. The first step a user takes when creating a listing on AptDeco is to submit a picture of their furniture. The editors at AptDeco will manually review the pictures, and decide if the images are of high enough quality to be edited and displayed on the front page of the listing.

Anomalies in time-series data give essential and often actionable information in many applications. In this paper we consider a model-free anomaly detection method for univariate time-series which adapts to non-stationarity in the data stream and provides probabilistic abnormality scores based on the conformal prediction paradigm. Despite its simplicity the method performs on par with complex prediction-based models on the Numenta Anomaly Detection benchmark and the Yahoo!

We address the statistical and optimization impacts of using classical sketch versus Hessian sketch to solve approximately the Matrix Ridge Regression (MRR) problem. Prior research has considered the effects of classical sketch on least squares regression (LSR), a strictly simpler problem. We establish that classical sketch has a similar effect upon the optimization properties of MRR as it does on those of LSR---namely, it recovers nearly optimal solutions. In contrast, Hessian sketch does not have this guarantee, instead, the approximation error is governed by a subtle interplay between the "mass" in the responses and the optimal objective value. For both types of approximations, the regularization in the sketched MRR problem gives it significantly different statistical properties from the sketched LSR problem. In particular, there is a bias-variance trade-off in sketched MRR that is not present in sketched LSR. We provide upper and lower bounds on the biases and variances of sketched MRR, these establish that the variance is significantly increased when classical sketches are used, while the bias is significantly increased when using Hessian sketches. Empirically, sketched MRR solutions can have risks that are higher by an order-of-magnitude than those of the optimal MRR solutions. We establish theoretically and empirically that model averaging greatly decreases this gap. Thus, in the distributed setting, sketching combined with model averaging is a powerful technique that quickly obtains near-optimal solutions to the MRR problem while greatly mitigating the statistical risks incurred by sketching.

Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of learning continuous semantic representations of algebraic and logical expressions. These networks are trained to represent semantic equivalence, even of expressions that are syntactically very different. The challenge is that semantic representations must be computed in a syntax-directed manner, because semantics is compositional, but at the same time, small changes in syntax can lead to very large changes in semantics, which can be difficult for continuous neural architectures. We perform an exhaustive evaluation on the task of checking equivalence on a highly diverse class of symbolic algebraic and boolean expression types, showing that our model significantly outperforms existing architectures.

State-level minimum Bayes risk (sMBR) training has become the de facto standard for sequence-level training of speech recognition acoustic models. It has an elegant formulation using the expectation semiring, and gives large improvements in word error rate (WER) over models trained solely using cross-entropy (CE) or connectionist temporal classification (CTC). sMBR training optimizes the expected number of frames at which the reference and hypothesized acoustic states differ. It may be preferable to optimize the expected WER, but WER does not interact well with the expectation semiring, and previous approaches based on computing expected WER exactly involve expanding the lattices used during training. In this paper we show how to perform optimization of the expected WER by sampling paths from the lattices used during conventional sMBR training. The gradient of the expected WER is itself an expectation, and so may be approximated using Monte Carlo sampling. We show experimentally that optimizing WER during acoustic model training gives 5% relative improvement in WER over a well-tuned sMBR baseline on a 2-channel query recognition task (Google Home).

Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques. A notable example is the determination of the smoothness parameter in splines. When the data are generated by a state space model, like in the spline case, efficient algorithms are available to evaluate the GCV score with complexity that scales linearly in the data set size. However, these methods are not amenable to on-line applications since they rely on forward and backward recursions. Hence, if the objective has been evaluated at time $t-1$ and new data arrive at time t, then O(t) operations are needed to update the GCV score. In this paper we instead show that the update cost is $O(1)$, thus paving the way to the on-line use of GCV. This result is obtained by deriving the novel GCV filter which extends the classical Kalman filter equations to efficiently propagate the GCV score over time. We also illustrate applications of the new filter in the context of state estimation and on-line regularized linear system identification.

We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability distributions is measured using the Wasserstein metric. Training samples contaminated with outliers skew the regression plane computed by least squares and thus impede outlier detection. Classical approaches, such as robust regression, remedy this problem by downweighting the contribution of atypical data points. In contrast, our Wasserstein DRO approach hedges against a family of distributions that are close to the empirical distribution. We show that the resulting formulation encompasses a class of models, which include the regularized Least Absolute Deviation (LAD) as a special case. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior, and the other concerns the discrepancy between the estimated and true regression planes. Extensive numerical results demonstrate the superiority of our approach to both robust regression and the regularized LAD in terms of estimation accuracy and outlier detection rates.