We summarize the potential impact that the European Union's new General Data Protection Regulation will have on the routine use of machine learning algorithms. 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 effectively create a "right to explanation," whereby a user can ask for an explanation of an algorithmic decision that was made about them. We argue that while this law will pose large challenges for industry, it highlights opportunities for computer scientists to take the lead in designing algorithms and evaluation frameworks which avoid discrimination and enable explanation.

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC as unknown parameters from measurements. Specifically, we focus on single linkage hierarchical clustering (SLHC) and study its geometry. We prove that under fairly reasonable conditions on the probability distribution governing measurements, SLHC is equivalent to maximum partial profile likelihood estimation (MPPLE) with some of the information contained in the data ignored. At the same time, we show that direct evaluation of SLHC on maximum likelihood estimation (MLE) of pairwise distances yields a consistent estimator. Consequently, a full MLE is expected to perform better than SLHC in getting the correct HC results for the ground truth metric.

A benefit of using ensembles of decision tree methods like gradient boosting is that they can automatically provide estimates of feature importance from a trained predictive model. In this post you will discover how you can estimate the importance of features for a predictive modeling problem using the XGBoost library in Python. Feature Importance and Feature Selection With XGBoost in Python Photo by Keith Roper, some rights reserved. XGBoost is the high performance implementation of gradient boosting that you can now access directly in Python. A benefit of using gradient boosting is that after the boosted trees are constructed, it is relatively straightforward to retrieve importance scores for each attribute.

As the election season rampages on, we categorize voters into broad demographics -- soccer moms, NASCAR dads, blacks, whites, ALICEs, yuppies -- in an attempt to understand and discuss this complex, churning electorate. In doing so we're tapping into something fundamental about how we perceive the world: not as a sequence of singular individuals, but rather as a massive set of overlapping taxonomies that, taken together, comprise an impressively structured human experience. With fewer than 20 yes/no queries on category membership we can often identify a single object amidst a staggering breadth of possibilities. We've grouped everything that we know to exist and the groupings themselves are the primary subject of our thoughts. We can go the other direction as well -- taking an object and placing it in its many groups.

K-means' goal is to reveal patterns within the data. Let's imagine that you have a database with millions of rows representing your customers' orders. You might want to use the K-means algorithm to gather your customers into different groups based on key characteristics. K-means is easy to implement; you just need to specify how many clusters you want. Here you should look at two measures.

Epilepsy is a chronic neurological condition that affects approximately 70 million people worldwide. Characterised by sudden bursts of excess electricity in the brain, manifesting as seizures, epilepsy is still not well understood when compared with other neurological disorders. Seizures often happen unexpectedly and attempting to predict them has been a research topic for the last 30 years. Electroencephalograms have been integral to these studies, as the recordings that they produce can capture the brain's electrical signals. The diagnosis of epilepsy is usually made by a neurologist, but can be difficult to make in the early stages.

Getting into machine learning (ml) can seem like an unachievable task from the outside. However, after dedicating one week to learning the basics of the subject, I found it to be much more accessible than I anticipated. This article is intended to give others who're interested in getting into ml a roadmap of how to get started, drawing from the experiences I made in my intro week. Before my machine learning week, I had been reading about the subject for a while, and had gone through half of Andrew Ng's course on Coursera and a few other theoretical courses. So I had a tiny bit of conceptual understanding of ml, though I was completely unable to transfer any of my knowledge into code.

An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample rate using stochastic gradient descent based optimization implemented in the state estimation filtering loop. The performance of the proposed method is compared with state-of-the-art Gaussian process based batch learning methods. Finally, it is shown that the state estimation performance significantly improves due to the online learning of state dynamics.

Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modeling gene expression collected on multiple tissues from the same individual: here the multivariate outcome is affected by dependencies acting not only at the level of the specific tissues, but also at the level of the whole body; existing methods that assume independence among graphs are not applicable in this case. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which affects all outcomes and thereby induces cross- graph dependence, and the category-specific layer, which represents graph-specific variation. We propose a graphical EM technique that estimates both layers jointly, establish estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simple one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results.

The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter have been proposed that incorporate linear approximations to nonlinear models, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, we argue that in cases where the dimensionality of observed variables greatly exceeds the dimensionality of state variables, a model for $p(\text{state}|\text{observation})$ proves both easier to learn and more accurate for latent space estimation. We derive and validate what we call the discriminative Kalman filter (DKF): a closed-form discriminative version of Bayesian filtering that readily incorporates off-the-shelf discriminative learning techniques. Further, we demonstrate that given mild assumptions, highly non-linear models for $p(\text{state}|\text{observation})$ can be specified. We motivate and validate on synthetic datasets and in neural decoding from non-human primates, showing substantial increases in decoding performance versus the standard Kalman filter.