If you've ever wondered how two or more things relate to each other, or if you've ever had your boss ask you to create a forecast or analyze relationships between variables, then learning regression would be worth your time. In this article, you'll learn the basics of simple linear regression - a tool commonly used in forecasting and financial analysis. We will begin by learning the core principles of regression, first learning about covariance and correlation, and then moving on to building and interpreting a regression output. A lot of software such as Microsoft Excel can do all the regression calculations and outputs for you, but it is still important to learn the underlying mechanics. At the center of regression is the relationship between two variables called the dependent and independent variables.

Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes have been successfully applied to model functional data in a variety of applications. A Gaussian Process is used to model the yield curve. The hyper-parameters of the Gaussian Process model are updated as the algorithm receives yield curve data. Yield curve data is typically available as a time series with a frequency of one day. We compare existing methods to forecast the yield curve with the proposed method. The results of this study showed that while a competing method (a multivariate time series method) performed well in forecasting the yields at the short term structure region of the yield curve, Gaussian Processes perform well in the medium and long term structure regions of the yield curve. Accuracy in the long term structure region of the yield curve has important practical implications. The Gaussian Process framework yields uncertainty and probability estimates directly in contrast to other competing methods. Analysts are frequently interested in this information. In this study the proposed method has been applied to yield curve forecasting, however it can be applied to model high frequency time series data or data streams in other domains.

Early and accurate identification of parkinsonian syndromes (PS) involving presynaptic degeneration from non-degenerative variants such as Scans Without Evidence of Dopaminergic Deficit (SWEDD) and tremor disorders, is important for effective patient management as the course, therapy and prognosis differ substantially between the two groups. In this study, we use Single Photon Emission Computed Tomography (SPECT) images from healthy normal, early PD and SWEDD subjects, as obtained from the Parkinson's Progression Markers Initiative (PPMI) database, and process them to compute shape- and surface fitting-based features for the three groups. We use these features to develop and compare various classification models that can discriminate between scans showing dopaminergic deficit, as in PD, from scans without the deficit, as in healthy normal or SWEDD. Along with it, we also compare these features with Striatal Binding Ratio (SBR)-based features, which are well-established and clinically used, by computing a feature importance score using Random forests technique. We observe that the Support Vector Machine (SVM) classifier gave the best performance with an accuracy of 97.29%. These features also showed higher importance than the SBR-based features. We infer from the study that shape analysis and surface fitting are useful and promising methods for extracting discriminatory features that can be used to develop diagnostic models that might have the potential to help clinicians in the diagnostic process.

This paper studies a new Bayesian algorithm for the joint reconstruction and classification of reflectance confocal microscopy (RCM) images, with application to the identification of human skin lentigo. The proposed Bayesian approach takes advantage of the distribution of the multiplicative speckle noise affecting the true reflectivity of these images and of appropriate priors for the unknown model parameters. A Markov chain Monte Carlo (MCMC) algorithm is proposed to jointly estimate the model parameters and the image of true reflectivity while classifying images according to the distribution of their reflectivity. Precisely, a Metropolis-within-Gibbs sampler is investigated to sample the posterior distribution of the Bayesian model associated with RCM images and to build estimators of its parameters, including labels indicating the class of each RCM image. The resulting algorithm is applied to synthetic data and to real images from a clinical study containing healthy and lentigo patients. The lentigo is a hyperplasia that affects the skin.

Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis of data streams and to the one-pass analysis of massive data sets. Applications include network traffic and latency analysis, real time fraud detection and high frequency trading. We introduce new techniques for online quantile estimation based on Hermite series estimators in the settings of static quantile estimation and dynamic quantile estimation. In the static quantile estimation setting we apply the existing Gauss-Hermite expansion in a novel manner. In particular, we exploit the fact that Gauss-Hermite coefficients can be updated in a sequential manner. To treat dynamic quantile estimation we introduce a novel expansion with an exponentially weighted estimator for the Gauss-Hermite coefficients which we term the Exponentially Weighted Gauss-Hermite (EWGH) expansion. These algorithms go beyond existing sequential quantile estimation algorithms in that they allow arbitrary quantiles (as opposed to pre-specified quantiles) to be estimated at any point in time. In doing so we provide a solution to online distribution function and online quantile function estimation on data streams. In particular we derive an analytical expression for the CDF and prove consistency results for the CDF under certain conditions. In addition we analyse the associated quantile estimator. Simulation studies and tests on real data reveal the Gauss-Hermite based algorithms to be competitive with a leading existing algorithm.

In this post, we are going to introduce you to the Support Vector Machine (SVM) machine learning algorithm. We will follow a similar process to our recent post Naive Bayes for Dummies; A Simple Explanation by keeping it short and not overly-technical. The aim is to give those of you who are new to machine learning a basic understanding of the key concepts of this algorithm. A Support Vector Machine (SVM) is a supervised machine learning algorithm that can be employed for both classification and regression purposes. SVMs are more commonly used in classification problems and as such, this is what we will focus on in this post.

Ten years on from its first 1.0 release, OpenCV (Short for Open Computer Vision) is a C library that lets you create software with real-time computer vision. Originally developed in Russia for Intel, it's fully open source and includes machine learning. It's BSD licensed so can be used freely. This is a very large library, with over 200 MB in various DLLs though you can also statically link to it if you prefer. It has several hundred algorithms in C with C, Python, Java and MATLAB interfaces and runs on Windows, Linux, Android, iOS and Mac OS.

Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.

Poisoning attack is identified as a severe security threat to machine learning algorithms. In many applications, for example, deep neural network (DNN) models collect public data as the inputs to perform re-training, where the input data can be poisoned. Although poisoning attack against support vector machines (SVM) has been extensively studied before, there is still very limited knowledge about how such attack can be implemented on neural networks (NN), especially DNNs. In this work, we first examine the possibility of applying traditional gradient-based method (named as the direct gradient method) to generate poisoned data against NNs by leveraging the gradient of the target model w.r.t. the normal data. We then propose a generative method to accelerate the generation rate of the poisoned data: an auto-encoder (generator) used to generate poisoned data is updated by a reward function of the loss, and the target NN model (discriminator) receives the poisoned data to calculate the loss w.r.t. the normal data. Our experiment results show that the generative method can speed up the poisoned data generation rate by up to 239.38x compared with the direct gradient method, with slightly lower model accuracy degradation. A countermeasure is also designed to detect such poisoning attack methods by checking the loss of the target model.

This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical adjustment of parametric forms) and highly accurate (they yield 5% error at most). We also highlight a few niche applications of these approximations, which arise in the context of, e.g., drift-diffusion models of decision making or non-parametric data clustering approaches. We provide these as examples of efficient alternatives to more tedious derivations that would be needed if one was to approach the underlying mathematical issues in a more formal way. We hope that this technical note will be helpful to modellers facing similar mathematical issues, although maybe stemming from different academic prospects.