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 Statistical Learning


Prediction of Daytime Hypoglycemic Events Using Continuous Glucose Monitoring Data and Classification Technique

arXiv.org Machine Learning

-- Daytime hypoglycemia should be accurately predicted to achieve normo glycemia and to avoid disastrous situations . Hypoglycemia, an abn ormally low blood glucose level, is divided into daytime hypogly cemia and nocturnal hypoglycemia . In this paper, we propose new predictor variables to predict daytime hypoglycemia using continuous glucose monitoring (CGM) data. We apply classification and regression tree (CART) as a prediction method . The evaluation results showed that our model wa s able to detect almost 80% of hypoglycemic events 15 min in advance, which was higher than the existing methods with similar conditions . T he proposed method might achieve a real - tim e prediction as well as can be e mbedded into BG monitoring device. Diabetes is one of the most common chronic diseases in the world, affecting 2.72 million individuals (10% of the population) in the Korea [1] and 29.1 million individuals (9.3% of the populat ion) in the USA with increasing incidence [2] . Diabetes can be th e cause of kidney failure, lower - limb amputations, and blindness among adults [2] . A chievement of excellent glycemia is most important task to diabetic patients in both type 1 and type 2 diabetes. D iabetic patient s should maintain euglycemic blood glucose (BG) levels while all day and be required the wisdom to avoid hyper - and hyp oglycemia [3] . Especially, the patients who treated w ith an insulin are at risk for developing hypoglycemia. Population - based data indicate that 30 - 40% o f people with type 1 diabetes ex perience an average of three episodes of severe hypoglycemia each year; those with insulin - treated type 2 diabetes experience about one episode of that each year. Also, individuals with type 1 diabetes experienced about 43 symptomatic (not only severe) episodes annually; insulin - treated individuals with type 2 diabetes experienced about 16 episodes annually [4] . The s ymptomatic hypoglycemic e pisode mean s that the patients feel the symptoms of s hakiness, sweating, hunger, irritability or headache [5] . H ypoglycemia is a significant challenge for a precise insulin therapy [6] .


Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)

arXiv.org Machine Learning

Learning DAG or Bayesian network models is an important problem in multi-variate causal inference. However, a number of challenges arises in learning large-scale DAG models including model identifiability and computational complexity since the space of directed graphs is huge. In this paper, we address these issues in a number of steps for a broad class of DAG models where the noise or variance is signal-dependent. Firstly we introduce a new class of identifiable DAG models, where each node has a distribution where the variance is a quadratic function of the mean (QVF DAG models). Our QVF DAG models include many interesting classes of distributions such as Poisson, Binomial, Geometric, Exponential, Gamma and many other distributions in which the noise variance depends on the mean. We prove that this class of QVF DAG models is identifiable, and introduce a new algorithm, the OverDispersion Scoring (ODS) algorithm, for learning large-scale QVF DAG models. Our algorithm is based on firstly learning the moralized or undirected graphical model representation of the DAG to reduce the DAG search-space, and then exploiting the quadratic variance property to learn the causal ordering. We show through theoretical results and simulations that our algorithm is statistically consistent in the high-dimensional p>n setting provided that the degree of the moralized graph is bounded and performs well compared to state-of-the-art DAG-learning algorithms.


A Network Perspective on Stratification of Multi-Label Data

arXiv.org Machine Learning

In the recent years, we have witnessed the development of multi-label classification methods which utilize the structure of the label space in a divide and conquer approach to improve classification performance and allow large data sets to be classified efficiently. Yet most of the available data sets have been provided in train/test splits that did not account for maintaining a distribution of higher-order relationships between labels among splits or folds. We present a new approach to stratifying multi-label data for classification purposes based on the iterative stratification approach proposed by Sechidis et. al. in an ECML PKDD 2011 paper. Our method extends the iterative approach to take into account second-order relationships between labels. Obtained results are evaluated using statistical properties of obtained strata as presented by Sechidis. We also propose new statistical measures relevant to second-order quality: label pairs distribution, the percentage of label pairs without positive evidence in folds and label pair - fold pairs that have no positive evidence for the label pair. We verify the impact of new methods on classification performance of Binary Relevance, Label Powerset and a fast greedy community detection based label space partitioning classifier. Random Forests serve as base classifiers. We check the variation of the number of communities obtained per fold, and the stability of their modularity score. Second-Order Iterative Stratification is compared to standard k-fold, label set, and iterative stratification. The proposed approach lowers the variance of classification quality, improves label pair oriented measures and example distribution while maintaining a competitive quality in label-oriented measures. We also witness an increase in stability of network characteristics.


Structured Sparse Modelling with Hierarchical GP

arXiv.org Machine Learning

Sparse regression problems arise often in various applications, e.g., model selection, compressive sensing, EEG source localisation and gene modelling [1], [2]. One of the Bayesian approaches to force the coefficients being zeros is the spike and slab prior [3]: each component is modelled as a mixture of spike, that is the delta-function in zero, and slab, that is some vague distribution. Following the Bayesian approach, latent variables that are indicators of spikes are added to the model [4] and the relevant distribution is placed over them [5]. In this model each component is modelled to be spike or slab independently. However, in many applications nonzero elements tend to appear in groups forming an unknown structure: wavelet coefficients of images are usually organised in trees [6], chromosomes have a spatial structure along the genome [2]. We propose an extension of the spike and slab model by imposing a hierarchical Gaussian process (GP) prior on the latent variables. Such hierarchical prior allows to model spatial structural dependencies for coefficients that can evolve in time. The new model is flexible as spatial and temporal dependencies are decoupled by different levels of the hierarchical GP prior.


A Siamese Deep Forest

arXiv.org Machine Learning

A Siamese Deep Forest (SDF) is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. It can be also regarded as an alternative to the well-known Siamese neural networks. The SDF uses a modified training set consisting of concatenated pairs of vectors. Moreover, it defines the class distributions in the deep forest as the weighted sum of the tree class probabilities such that the weights are determined in order to reduce distances between similar pairs and to increase them between dissimilar points. We show that the weights can be obtained by solving a quadratic optimization problem. The SDF aims to prevent overfitting which takes place in neural networks when only limited training data are available. The numerical experiments illustrate the proposed distance metric method.


Online Natural Gradient as a Kalman Filter

arXiv.org Machine Learning

We establish a full relationship between Kalman filtering and Amari's natural gradient in statistical learning. Namely, using an online natural gradient descent on data log-likelihood to evaluate the parameter of a probabilistic model from a series of observations, is exactly equivalent to using an extended Kalman filter to estimate the parameter (assumed to have constant dynamics). In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant settings for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix. The Appendix contains a reminder on exponential families.


Learning Representations by Stochastic Meta-Gradient Descent in Neural Networks

arXiv.org Machine Learning

Representations are fundamental to artificial intelligence. The performance of a learning system depends on the type of representation used for representing the data. Typically, these representations are hand-engineered using domain knowledge. More recently, the trend is to learn these representations through stochastic gradient descent in multi-layer neural networks, which is called backprop. Learning the representations directly from the incoming data stream reduces the human labour involved in designing a learning system. More importantly, this allows in scaling of a learning system for difficult tasks. In this paper, we introduce a new incremental learning algorithm called crossprop, which learns incoming weights of hidden units based on the meta-gradient descent approach, that was previously introduced by Sutton (1992) and Schraudolph (1999) for learning step-sizes. The final update equation introduces an additional memory parameter for each of these weights and generalizes the backprop update equation. From our experiments, we show that crossprop learns and reuses its feature representation while tackling new and unseen tasks whereas backprop relearns a new feature representation.


100 Data Science Interview Questions and Answers (General) for 2017

#artificialintelligence

In collaboration with data scientists, industry experts and top counsellors, we have put together a list of general data science interview questions and answers to help you with your preparation in applying for data science jobs. This also includes a list of open ended questions that interviewers ask to get a feel of how often and how quickly you can think on your feet.There are some data analyst interview questions in this blog which can also be asked in a data science interview. These kind of analytics interview questions also measure if you were successful in applying data science techniques to real life problems. If you would like more information about Online Data Science course, please click the orange "Request Info" button on top of this page. Data Science is not an easy field to get into. This is something all data scientists will agree on. Apart from having a degree in mathematics/statistics or engineering, a data scientist also needs to go through intense training to develop all the skills required for this field. Apart from the degree/diploma and the training, it is important to prepare the right resume for a data science job, and to be well versed with the data science interview questions and answers. Consider our top 100 Data Science Interview Questions and Answers as a starting point for your data scientist interview preparation.


Introduction to Principal Component Analysis

@machinelearnbot

Here is a short overview about how PCA (principal component analysis) works for dimension reduction, that is, to select k features (also called variables) among a larger set of n features, with k much smaller than n. This smaller set of k features built with PCA is the best subset of k features, in the sense that it minimizes the variance of the residual noise when fitting data to a linear model. Note that PCA transforms the initial features into new ones, that are linear combinations of the original features.


will wolf

#artificialintelligence

The original goal of this post was to explore the relationship between the softmax and sigmoid functions. In truth, this relationship had always seemed just out of reach: "One has an exponent in the numerator! One has a 1 in the denominator!" And of course, the two have different names. Once derived, I quickly realized how this relationship backed out into a more general modeling framework motivated by the conditional probability axiom itself.