We introduce a machine learning approach for extracting fine-grained representations of protein evolution from molecular dynamics datasets. Metastable switching linear dynamical systems extend standard switching models with a physically-inspired stability constraint. This constraint enables the learning of nuanced representations of protein dynamics that closely match physical reality. We derive an EM algorithm for learning, where the E-step extends the forward-backward algorithm for HMMs and the M-step requires the solution of large biconvex optimization problems. We construct an approximate semidefinite program solver based on the Frank-Wolfe algorithm and use it to solve the M-step. We apply our EM algorithm to learn accurate dynamics from large simulation datasets for the opioid peptide met-enkephalin and the proto-oncogene Src-kinase. Our learned models demonstrate significant improvements in temporal coherence over HMMs and standard switching models for met-enkephalin, and sample transition paths (possibly useful in rational drug design) for Src-kinase.

Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual series. Furthermore, our algorithm is extended to take into account individual autocorrelation to provide better estimation, using a recent convex relaxation of quadratically constrained quadratic program. Extensive experiments on synthetic and real-world electricity consumption datasets illustrate the effectiveness of our matrix recovery algorithms.

Tests for Esophageal cancer can be expensive, uncomfortable and can have side effects. For many patients, we can predict non-existence of disease with 100% certainty, just using demographics, lifestyle, and medical history information. Our objective is to devise a general methodology for customizing tests using user preferences so that expensive or uncomfortable tests can be avoided. We propose to use classifiers trained from electronic health records (EHR) for selection of tests. The key idea is to design classifiers with 100% false normal rates, possibly at the cost higher false abnormals. We compare Naive Bayes classification (NB), Random Forests (RF), Support Vector Machines (SVM) and Logistic Regression (LR), and find kernel Logistic regression to be most suitable for the task. We propose an algorithm for finding the best probability threshold for kernel LR, based on test set accuracy. Using the proposed algorithm, we describe schemes for selecting tests, which appear as features in the automatic classification algorithm, using preferences on costs and discomfort of the users. We test our methodology with EHRs collected for more than 3000 patients, as a part of project carried out by a reputed hospital in Mumbai, India. Kernel SVM and kernel LR with a polynomial kernel of degree 3, yields an accuracy of 99.8% and sensitivity 100%, without the MP features, i.e. using only clinical tests. We demonstrate our test selection algorithm using two case studies, one using cost of clinical tests, and other using "discomfort" values for clinical tests. We compute the test sets corresponding to the lowest false abnormals for each criterion described above, using exhaustive enumeration of 15 clinical tests. The sets turn out to different, substantiating our claim that one can customize test sets based on user preferences.

A methodology for binary classification of EEG records which correspond to different mental states is proposed. This model-free methodology is based on our theory of the $\epsilon$-complexity of continuous functions which is extended here (see Appendix) to the case of vector functions. This extension permits us to handle multichannel EEG recordings. The essence of the methodology is to use the $\epsilon$-complexity coefficients as features to classify (using well known classifiers) different types of vector functions representing EEG-records corresponding to different types of mental states. We apply our methodology to the problem of classification of multichannel EEG-records related to a group of healthy adolescents and a group of adolescents with schizophrenia. We found that our methodology permits accurate classification of the data in the four-dimensional feather space of the $\epsilon$-complexity coefficients.

I just completed a take home assessment as part of the interview process for a company. I was told I didn't pass because my answer lacked proper training and test sets The data set consisted of a mix of categorical and numerical predictors, with the dependent variable being a numerical variable. I then removed all rows with NA values and generated boxplots for each predictor. For one variable, I replaced all of its outliers with the median. For some other variables that indicated percentage values, I did not remove the outliers because they did not seem like obvious outliers (for example, the boxplot showed that values greater than .1 were outliers, but all of those outliers still ranged from 0 to 1 so I didn't think they were typos) I then ran a Lasso linear regression model.

The City and County of San Francisco had launched an official open data portal called SF OpenData in 2009 as a product of its official open data program, DataSF. The portal contains hundreds of city datasets for use by developers, analysts, residents and more. Under the category of Public Safety, the portal contains the list of SFPD Incidents since Jan 1, 2003. In this post I have done an exploratory time-series analysis on the crime incidents dataset to see if there are any patterns. The data for this analysis was downloaded from the publicly available dataset from the City and County of San Francisco's OpenData website SF OpenData.

When millions of people across the world tuned in to watch DeepMind's machine beat the human Go world champion Lee Sedol, they also witnessed a historic victory for open-source. DeepMind used a scientific computing framework called Torch extensively in the development and execution of AlphaGo's neural networks. Torch was first released back in 2002 under a BSD open-source license with algorithms that are still commonly used by data scientists such as multi-layer perceptrons, support vector machines and K-nearest neighbours. Torch also supported ensembles -- a popular technique that combines the output of multiple algorithms, usually with a weighted average. It's not just open-source software that contributed to the growth of machine learning.

Consequently, there is an equivalence between parameter averaging and update-based data parallelism, when parameters are updated synchronously (this last part is key). This equivalence also holds for multiple averaging steps and other updaters (not just simple SGD). Update-based data parallelism becomes more interesting (and arguably more useful) when we relax the synchronous update requirement. That is, by allowing the updates Wi,j to be applied to the parameter vector as soon as they are computed (instead of waiting for N 1 iterations by all workers), we obtain asynchronous stochastic gradient descent algorithm. These benefits are not without cost, however. By introducing asynchronous updates to the parameter vector, we introduce a new problem, known as the stale gradient problem.

In my previous blog I have explained about linear regression. In today's post I will explain about logistic regression. Consider a scenario where we need to predict a medical condition of a patient (HBP),HAVE HIGH BP or NO HIGH BP, based on some observed symptoms – Age, weight, Issmoking, Systolic value, Diastolic value, RACE, etc.. In this scenario we have to build a model which takes the above mentioned symptoms as input values and HBP as response variable. Note that the response variable (HBP) is a value among a fixed set of classes, HAVE HIGH BP or NO HIGH BP.

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in their fundamental structure. It is often not clear which function structure to choose, for instance to decide between a squared exponential and a rational quadratic kernel. Based on the principle of approximation set coding, we develop a framework for model selection to rank kernels for Gaussian process regression. In our experiments approximation set coding shows promise to become a model selection criterion competitive with maximum evidence (also called marginal likelihood) and leave-one-out cross-validation.