Yesterday I gave a super duper high level 12 minutes presentation about some issues of bias in AI. I should emphasize (if it's not clear) that this is something I am not an expert in; most of what I know is by reading great papers by other people (there is a completely non-academic sample at the end of this post). This blog post is a variant of that presentation. Structure: most of the images below are prompts for talking points, which are generally written below the corresponding image. I think I managed to link all the images to the original source (let me know if I missed one!). Automated Decision Making is Part of Our Lives To me, AI is largely the study of automated decision making, and the investment therein has been growing at a dramatic rate. The last time I taught this class was in 2012. The amount that's changed since there is incredible.

The idea of cross-validation is to split the data into N subsets, to put one subset aside, to estimate parameters of the model from the remaining N-1 subsets, and to use the retained subset to estimate the error of the model. Such a process is repeated N times - with each of the N subsets being used as the validation set . Then the values of the errors obtained in such N steps are combined to provide the final estimate of the model error. The cross-validation is used in various classification and prediction procedures, such as regression analysis, discriminant analysis, neural networks and classification and regression trees (CART) . The goal is to improve the quality of the decision that is made from the outcome of the study on the basis of statistical methods, and to ensure that maximum information is obtained from scarce experimental data.

Data science is fast becoming a critical skill for developers and managers across industries, and it looks like a lot of fun as well. But it's pretty complicated - there are a lot of engineering and analytical options to navigate, and it's hard to know if you're doing it right or where the bear traps lie. In this series we explore ways in to making sense of data science - understanding where it's needed and where it's not, and how to make it an asset for you, from people who've been there and done it. This InfoQ article is part of the series "Getting A Handle On Data Science" . You can subscribe to receive notifications via RSS. Enterprises are increasingly realising that many of their most pressing business problems could be tackled with the application of a little data science.

Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within-and across-subject predictions, on multiple datasets --anatomical and functional MRI and MEG-- and simulations. Theory and experiments outline that the popular " leave-one-out " strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be more favorable to use sane defaults, in particular for non-sparse decoders.

We consider the validation of prognostic diagnostic tests that predict two prognostic subgroups (high-risk vs low-risk) for a given disease or treatment. When comparing survival curves between two prognostic subgroups the possibility of misclassification arises, i.e. a patient predicted as high-risk might be de facto low-risk and vice versa. This is a fundamental difference from comparing survival curves between two populations (e.g. control vs treatment in RCT), where there is not an option of misclassification between members of populations. We show that there is a relationship between prognostic subgroups' survival estimates at a time point and positive and negative predictive values in the classification settings. Consequently, the prevalence needs to be taken into account when validating the survival of prognostic subgroups at a time point. Our findings question current methods of comparing survival curves between prognostic subgroups in the validation set because they do not take into account the survival rates of the population.

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the sample size, defies most existing work. This paper introduces a novel and computationally feasible multivariate screening and classification method for ultrahigh-dimensional data. Leveraging inter-feature correlations, the proposed method enables detection of marginally weak and sparse signals and recovery of the true informative feature set, and achieves asymptotic optimal misclassification rates. We also show that the proposed procedure provides more powerful discovery boundaries compared to those in \citet{CaiSun:2014} and \citet{JJin:2009}. The performance of the proposed procedure is evaluated using simulation studies and demonstrated via classification of patients with different post-transplantation renal functional types.

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled dataset is often not available. In this paper, we show that, with additional samples coming only from the positive class, the class prior of the unlabeled dataset can be estimated correctly. Our key idea is to use properly penalized divergences for model fitting to cancel the error caused by the absence of negative samples. We further show that the use of the penalized $L_1$-distance gives a computationally efficient algorithm with an analytic solution. The consistency, stability, and estimation error are theoretically analyzed. Finally, we experimentally demonstrate the usefulness of the proposed method.

Think of a regression model mapping a number of features onto a real number (potentially a probability). The resulting real number can then be mapped on one of two classes, depending on whether this predicted number is greater or lower than some choosable threshold. Let's take for example a logistic regression and data on the survivorship of the Titanic accident to introduce the relevant concepts which will lead naturally to the ROC (Receiver Operating Characteristic) and its AUC or AUROC (Area Under ROC Curve). Every record in the data set represents a passenger – providing information on her/his age, gender, class, number of siblings/spouses aboard (sibsp), number of parents/children aboard (parch) and, of course, whether s/he survived the accident. The logistic regression model is tested on batches of 10 cases with a model trained on the remaining N-10 cases – the test batches form a partition of the data. In short, Leave-10-out CV has been applied to arrive at more accurate estimation of the out-of-sample error rates.

Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the shrinkage framework to Nonlinear Shrinkage (NLS), a more powerful covariance estimator based on Random Matrix Theory. Our contribution shows that, contrary to claims in the literature, cross-validation based covariance matrix estimation (CVC) yields comparable performance at strongly reduced complexity and runtime. On two real world data sets, we show that the CVC estimator yields superior results than competing shrinkage and factor based methods.

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampered by two important problems: the high computational cost involved, as two kernel matrices of the sample size have to be computed and stored, and the interpretability of the measure, which remains hidden behind the implicit feature map. We here address these two issues. We introduce the Sensitivity Maps (SMs) for the Hilbert-Schmidt independence criterion (HSIC). Sensitivity maps allow us to explicitly analyze and visualize the relative relevance of both examples and features on the dependence measure. We also present the randomized HSIC (RHSIC) and its corresponding sensitivity maps to cope with large scale problems. We build upon the framework of random features and the Bochner's theorem to approximate the involved kernels in the canonical HSIC. The power of the RHSIC measure scales favourably with the number of samples, and it approximates HSIC and the sensitivity maps efficiently. Convergence bounds of both the measure and the sensitivity map are also provided. Our proposal is illustrated in synthetic examples, and challenging real problems of dependence estimation, feature selection, and causal inference from empirical data.