General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that offer guarantees regarding validity. In this paper we provide a detailed description of a computationally efficient conformal procedure for Kernel Ridge Regression (KRR), and conduct a comparative numerical study to see how well conformal regions perform against the Bayesian confidence sets. The results suggest that conformalized KRR can yield predictive confidence regions with specified coverage rate, which is essential in constructing anomaly detection systems based on predictive models.

Principal component analysis (PCA) is a technique to find orthonormal vectors, which are a linear combination of the attributes of the data, that explain the variance structure of the data [12]. Since a few orthonormal vectors usually explain most of the variance, PCA is often used to reduce dimension of the data by keeping only a few of the orthonormal vectors. These orthonormal vectors are called principal components (PCs). For dimensionality reduction, we are given target dimension p, the number of PCs. To measure accuracy, given p principal components, first, the original data is projected into the lower dimension using the PCs. Next, the projected data in the lower dimension is lifted to the original dimension using the PCs. Observe that this procedure causes loss of some information if p is smaller than the dimension of the original attribute space. The reconstruction error is defined by the difference between the projected-and-lifted data and the original data. To select the best p PCs, the following two objective functions are usually used: [P1] minimization of the reconstruction error, [P2] maximization of the variance of the projected data.

We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix and therefore subsequent processing, such as PCA or K-means, is significantly faster, especially in a distributed-data setting. Furthermore, the sampling is single-pass and applicable to streaming data. The sampling mechanism is a variant of previous methods proposed in the literature combined with a randomized preconditioning to smooth the data. We provide guarantees for PCA in terms of the covariance matrix, and guarantees for K-means in terms of the error in the center estimators at a given step. We present numerical evidence to show both that our bounds are nearly tight and that our algorithms provide a real benefit when applied to standard test data sets, as well as providing certain benefits over related sampling approaches.

I have decided to focus on the field of healthcare and classify whether or not a patient has Parkinson's disease based on their vocalization data. For context, Parkinson's is a progressive disease that causes the degeneration of the brain, leading to both motor and cognitive problems. It is thus reasonable to assume a correlation between a patient's ability to speak and their progression into Parkinson's as these capabilities regress. The data set I worked with was obtained through a 2008 study by the journal, IEEE Transactions on Biomedical Engineering, of how various parameters of voice frequency can help classify if a patient is suffering from Parkinson's. By performing a classification on this data, I hope to prove that vocalization tests are indeed a well suited way to diagnose a patient for this disease.

I've got a collection of historic log files for a process that repeats daily, roughly the same each day. I want an NN that, from the moment that the daily process starts, estimates what time the whole process will finally complete. As the daily process progresses, the estimate should become more accurate and converge on the actual completion time as soon as possible. A degree of confidence in the prediction would be useful too. The daily process is a collection of mostly serial subprocesses.

A supervised machine learning model aims to learn a function f(x) y from a list of training pairs (x1,y1), (x2,y2), … for which data are recorded (Fig 1B). One typical application in biology is to predict the viability of a cancer cell line when exposed to a chosen drug (Menden et al, 2013; Eduati et al, 2015). The input features (x) would capture somatic sequence variants of the cell line, chemical make?up of the drug and its concentration, which together with the measured viability (output label y) can be used to train a support vector machine, a random forest classifier or a related method (functional relationship f). Given a new cell line (unlabelled data sample x*) in the future, the learnt function predicts its survival (output label y*) by calculating f(x*), even if f resembles more of a black box, and its inner workings of why particular mutation combinations influence cell growth are not easily interpreted. Both regression (where y is a real number) and classification (where y is a categorical class label) can be viewed in this way. As a counterpart, unsupervised machine learning approaches aim to discover patterns from the data samples x themselves, without the need for output labels y. Methods such as clustering, principal component analysis and outlier detection are typical examples of unsupervised models applied to biological data. The inputs x, calculated from the raw data, represent what the model "sees about the world", and their choice is highly problem?specific (Fig 1C). Deriving most informative features is essential for performance, but the process can be labour?intensive

Ensemble methods for classification and clustering have been effectively used for decades, while ensemble learning for outlier detection has only been studied recently. In this work, we design a new ensemble approach for outlier detection in multi-dimensional point data, which provides improved accuracy by reducing error through both bias and variance. Although classification and outlier detection appear as different problems, their theoretical underpinnings are quite similar in terms of the bias-variance trade-off [1], where outlier detection is considered as a binary classification task with unobserved labels but a similar bias-variance decomposition of error. In this paper, we propose a sequential ensemble approach called CARE that employs a two-phase aggregation of the intermediate results in each iteration to reach the final outcome. Unlike existing outlier ensembles which solely incorporate a parallel framework by aggregating the outcomes of independent base detectors to reduce variance, our ensemble incorporates both the parallel and sequential building blocks to reduce bias as well as variance by ($i$) successively eliminating outliers from the original dataset to build a better data model on which outlierness is estimated (sequentially), and ($ii$) combining the results from individual base detectors and across iterations (parallelly). Through extensive experiments on sixteen real-world datasets mainly from the UCI machine learning repository [2], we show that CARE performs significantly better than or at least similar to the individual baselines. We also compare CARE with the state-of-the-art outlier ensembles where it also provides significant improvement when it is the winner and remains close otherwise.

The electronic health record (EHR) provides an unprecedented opportunity to build actionable tools to support physicians at the point of care. In this paper, we investigate survival analysis in the context of EHR data. We introduce deep survival analysis, a hierarchical generative approach to survival analysis. It departs from previous approaches in two primary ways: (1) all observations, including covariates, are modeled jointly conditioned on a rich latent structure; and (2) the observations are aligned by their failure time, rather than by an arbitrary time zero as in traditional survival analysis. Further, it (3) scalably handles heterogeneous (continuous and discrete) data types that occur in the EHR. We validate deep survival analysis model by stratifying patients according to risk of developing coronary heart disease (CHD). Specifically, we study a dataset of 313,000 patients corresponding to 5.5 million months of observations. When compared to the clinically validated Framingham CHD risk score, deep survival analysis is significantly superior in stratifying patients according to their risk.

Ladies and gentlemen, place your bets, today we are going to do our best to beat one of the most frightening opponents that you can face in finance: a monkey. As you probably already know, in this blog we are all quite obsessed with predicting trends and returns, you can find other nice attempts in'Markov Switching Regimes say… bear or bullish?' by mplanaslasa or'Predict returns using historical patterns' by fjrodriguez2. Today, we are trying to predict the sign of tomorrow's return for different currency pairs, and I can assure you that a monkey making random bets on the sign and getting it right 50% of the time is going to be a tough benchmark. We are going to use an off the shelf machine learning algorithm, the support vector classifier. Support Vector Machines are an incredibly powerful method to solve regression and classification tasks.

I recently came across this question on Cross Validated, and I thought it offered a great opportunity to use R and ggplot2 to explore, in depth, the assumptions underlying the k-means algorithm. The question, and my response, follow. K-means is a widely used method in cluster analysis. In my understanding, this method does NOT require ANY assumptions, i.e., give me a data set and a pre-specified number of clusters, k, then I just apply this algorithm which minimize the SSE, the within cluster square error. So k-means, it is essentially an optimization problem.