Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can play a crucial role in powering meaningful scientific discoveries through the understanding of important differences among subpopulations of interest. In this paper, we exploit multiple networks with Gaussian graphs to encode the connectivity patterns of a large number of features on the subpopulations. To uncover the heterogeneity of these structures across subpopulations, we suggest a new framework of tuning-free heterogeneity pursuit (THP) via large-scale inference, where the number of networks is allowed to diverge. In particular, two new tests, the chi-based test and the linear functional-based test, are introduced and their asymptotic null distributions are established. Under mild regularity conditions, we establish that both tests are optimal in achieving the testable region boundary and the sample size requirement for the latter test is minimal. Both theoretical guarantees and the tuning-free feature stem from efficient multiple-network estimation by our newly suggested approach of heterogeneous group square-root Lasso (HGSL) for high-dimensional multi-response regression with heterogeneous noises. To solve this convex program, we further introduce a tuning-free algorithm that is scalable and enjoys provable convergence to the global optimum. Both computational and theoretical advantages of our procedure are elucidated through simulation and real data examples.

Hey, thankyou for the input but I am new to the field. I started it this summer. Until now I have only worked on linear,logistic regression and k-nearest neighbors. I'm looking forward to work on a project on these algorithm before I go deep in field.

We provide an overview and perform an experimental comparison between the famous iterative reconstruction methods in terms of reconstruction quality in sparse view situations. We then derive the proximal operators for the four best methods. We show the flexibility of our framework by deriving solvers for two noise models: Gaussian and Poisson; and by plugging in three powerful regularizers. We compare our framework to state of the art methods, and show superior quality on both synthetic and real datasets.

Michael Jordan, Jason Lee, and Yun Yang just arXived a paper with their proposal on handling large datasets through distributed computing, thus contributing to the currently very active research topic of approximate solutions in large Bayesian models. The core of the proposal is summarised by the screenshot above, where the approximate likelihood replaces the exact likelihood with a first order Taylor expansion. The first term is the likelihood computed for a given subsample (or a given thread) at a ratio of one to N and the difference of the gradients is only computed once at a good enough guess. While the paper also considers M-estimators and non-Bayesian settings, the Bayesian part thus consists in running a regular MCMC when the log-target is approximated by the above. I first thought this proposal amounted to a Gaussian approximation à la Simon Wood or to an INLA approach but this is not the case: the first term of the approximate likelihood is exact and hence can be of any form, while the scalar product is linear in?, providing a sort of first order approximation, albeit frozen at the chosen starting value.

Finding an accurate machine learning model is not the end of the project. In this post you will discover how to save and load your machine learning model in Python using scikit-learn. This allows you to save your model to file and load it later in order to make predictions. Save and Load Machine Learning Models in Python with scikit-learn Photo by Christine, some rights reserved. Pickle is the standard way of serializing objects in Python.

I have created a model in R using data with a lot of categorical data and it works well enough (70% classification rate). I need to transfer the code to python for launching to production, however when i transfer the code the results decrease considerably (40% classification rate). I think it may be to do with how I encode the categorical data, any ideas?

In my latest video blog (6.25 minutes), I provide an overview of Survival Analysis, an extremely useful branch of statistics. You can access the video here. If you enjoy the video, please leave a comment on my blog or by following me on Twitter @VRaoRao.

Classification is one of the major problems that we solve while working on standard business problems across industries. In this article we'll be discussing the major three of the many techniques used for the same, Logistic Regression, Decision Trees and Support Vector Machines [SVM]. All of the above listed algorithms are used in classification [ SVM and Decision Trees are also used for regression, but we are not discussing that today!]. Time and again I have seen people asking which one to choose for their particular problem. Classical and the most correct but least satisfying response to that question is "it depends!".

Real music signals are highly variable, yet they have strong statistical structure. Prior information about the underlying physical mechanisms by which sounds are generated and rules by which complex sound structure is constructed (notes, chords, a complete musical score), can be naturally unified using Bayesian modelling techniques. Typically algorithms for Automatic Music Transcription independently carry out individual tasks such as multiple-F0 detection and beat tracking. The challenge remains to perform joint estimation of all parameters. We present a Bayesian approach for modelling music audio, and content analysis. The proposed methodology based on Gaussian processes seeks joint estimation of multiple music concepts by incorporating into the kernel prior information about non-stationary behaviour, dynamics, and rich spectral content present in the modelled music signal. We illustrate the benefits of this approach via two tasks: pitch estimation, and inferring missing segments in a polyphonic audio recording.

We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizations. However, in many real-world datasets, variables clearly have positive dependencies. For example, the airport delay time in New York---modeled as an exponential distribution---is positively related to the delay time in Boston. With this motivation, we give an example of our model class derived from the univariate exponential distribution that allows for almost arbitrary positive and negative dependencies with only a mild condition on the parameter matrix---a condition akin to the positive definiteness of the Gaussian covariance matrix. Our Poisson generalization allows for both positive and negative dependencies without any constraints on the parameter values. We also develop parameter estimation methods using node-wise regressions with $\ell_1$ regularization and likelihood approximation methods using sampling. Finally, we demonstrate our exponential generalization on a synthetic dataset and a real-world dataset of airport delay times.