Data Discovery: The first phase involves analysis on historical data to build the machine learning model. Analytics Using the Model: The second phase uses the model in production on live events. Data Discovery: The first phase involves analysis on historical data to build the machine learning model. Analytics Using the Model: The second phase uses the model in production on live events. In this first post, I'll help you get started using Apache Spark's machine learning K-means algorithm to cluster Uber data based on location.

This paper describes a computational model, called the Dirichlet process Gaussian mixture model with latent joints (DPGMM-LJ), that can find latent tree structure embedded in data distribution in an unsupervised manner. By combining DPGMM-LJ and a pre-existing body map formation method, we propose a method that enables an agent having multi-link body structure to discover its kinematic structure, i.e., body schema, from tactile information alone. The DPGMM-LJ is a probabilistic model based on Bayesian nonparametrics and an extension of Dirichlet process Gaussian mixture model (DPGMM). In a simulation experiment, we used a simple fetus model that had five body parts and performed structured random movements in a womb-like environment. It was shown that the method could estimate the number of body parts and kinematic structures without any pre-existing knowledge in many cases. Another experiment showed that the degree of motor coordination in random movements affects the result of body schema formation strongly. It is confirmed that the accuracy rate for body schema estimation had the highest value 84.6% when the ratio of motor coordination was 0.9 in our setting. These results suggest that kinematic structure can be estimated from tactile information obtained by a fetus moving randomly in a womb without any visual information even though its accuracy was not so high. They also suggest that a certain degree of motor coordination in random movements and the sufficient dimension of state space that represents the body map are important to estimate body schema correctly.

We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's \rho to extreme ranks. Our main contribution is the derivation of a non-parametric estimator for rank aggregation based on multivariate extensions of Spearman's \rho, which measures correlation between a set of ranked lists. Multivariate Spearman's \rho is defined using copulas, and we show that the geometric mean of normalised ranks maximises multivariate correlation. Motivated by this, we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution. When only the best or worst elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman's \rho. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008.

We aim to create a framework for transfer learning using latent factor models to learn the dependence structure between a larger source dataset and a target dataset. The methodology is motivated by our goal of building a risk-assessment model for surgery patients, using both institutional and national surgical outcomes data. The national surgical outcomes data is collected through NSQIP (National Surgery Quality Improvement Program), a database housing almost 4 million patients from over 700 different hospitals. We build a latent factor model with a hierarchical prior on the loadings matrix to appropriately account for the different covariance structure in our data. We extend this model to handle more complex relationships between the populations by deriving a scale mixture formulation using stick-breaking properties. Our model provides a transfer learning framework that utilizes all information from both the source and target data, while modeling the underlying inherent differences between them.

We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately balance the load between the available machines to minimize the average SGD iteration time. Our experiments consider setups with over thirty parameters. Traditional Bayesian optimization, which uses a Gaussian process as its model, is not well suited to such high dimensional domains. To reduce convergence time, we exploit the available structure. We design a probabilistic model which simulates the behavior of distributed SGD and use it within Bayesian optimization. Our model can exploit many runtime measurements for inference per evaluation of the objective function. Our experiments show that our resulting optimizer converges to efficient configurations within ten iterations, the optimized configurations outperform those found by generic optimizer in thirty iterations by up to 2X.

We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The proposed approach combines appealing features of finite basis representation and smoothing penalties for non-parametric estimation. In particular, in the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions posses different levels of complexity. On the other hand, a smoothing spline type penalty on the component functions is adaptive but does not offer a parsimonious representation of the estimated function. The proposed approach simultaneously achieves parsimony and adaptivity in a computationally efficient framework. We demonstrate these properties through empirical studies on both real and simulated datasets. We show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. The proposed method is implemented using an efficient algorithm that scales similarly to the Lasso with the number of covariates and samples size.

Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed individually because of their small sample size. Bayesian nonparametric modelling approaches can be used to model such datasets given their ability to flexibly share information across groups. In this paper, we will compare three popular Bayesian nonparametric methods for modelling the survival functions of heterogeneous groups. Specifically, we will first compare the modelling accuracy of the Dirichlet process, the hierarchical Dirichlet process, and the nested Dirichlet process on simulated datasets of different sizes, where group survival curves differ in shape or in expectation. We, then, will compare the models on a real-world injury dataset.

Clustering is an important problem which is prevalent in a variety of real world problems. One of the first and widely applied clustering algorithms is k-means, which was named by James MacQueen [15], but was proposed by Hugo Steinhaus [23] even before. Despite being half a century old, k-means has been widely used and analyzed under various settings. One major drawback of k-means is its incapability to separate clusters that are non-linearly separated. This can be alleviated by mapping the data to a high dimensional feature space and do clustering on top of the feature space [21, 9, 12], which is generally called kernel-based methods. For instance, the widely-used spectral clustering [22, 17] is an algorithm to calculate top eigenvectors of a kernel matrix of affinities, followed by a k-means on the top r eigenvectors. The consistency of spectral clustering is analyzed by [25].

We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin bounds known for both standard multi-class and general structured prediction problems. Our guarantees are expressed in terms of a data-dependent complexity measure, factor graph complexity, which we show can be estimated from data and bounded in terms of familiar quantities. We further extend our theory by leveraging the principle of Voted Risk Minimization (VRM) and show that learning is possible even with complex factor graphs. We present new learning bounds for this advanced setting, which we use to design two new algorithms, Voted Conditional Random Field (VCRF) and Voted Structured Boosting (StructBoost). These algorithms can make use of complex features and factor graphs and yet benefit from favorable learning guarantees. We also report the results of experiments with VCRF on several datasets to validate our theory.

The number of clusters steadily decreases (7 at 20s [ 167 iterations], 6 at 40s [ 333 iterations], 5 at the end [500 iterations]) Around the middle of the video you see that the clusters appear to be fairly stable, however more iterations result in a significant change in cluster location and number. A local minimum was detected, however it was not the global minimum. One cluster is especially small (and potentially suspect) at the end of the iterations in this simulation One of the clusters is unstable: points are exchanging between it and a nearby cluster - further iterations may reduce the number of clusters through consolidation. There is a lot more movement of points within the z dimension than along x or y. This would be worth investigating as a potential issue with the clustering algorithm or visualization - or perhaps something interesting is going on!