To develop a proof-of-concept convolutional neural network (CNN) to synthesize T2 maps in right lateral femoral condyle articular cartilage from anatomic MR images by using a conditional generative adversarial network (cGAN). In this retrospective study, anatomic images (from turbo spin-echo and double-echo in steady-state scans) of the right knee of 4621 patients included in the 2004–2006 Osteoarthritis Initiative were used as input to a cGAN-based CNN, and a predicted CNN T2 was generated as output. These patients included men and women of all ethnicities, aged 45–79 years, with or at high risk for knee osteoarthritis incidence or progression who were recruited at four separate centers in the United States. These data were split into 3703 (80%) for training, 462 (10%) for validation, and 456 (10%) for testing. Linear regression analysis was performed between the multiecho spin-echo (MESE) and CNN T2 in the test dataset.

On top of recommending the excellent autobiography of Stanislaw Ulam, this post is about using the software Stan, but not directly to perform inference, instead to obtain R functions to evaluate a target's probability density function and its gradient. With which, one can implement custom methods, while still benefiting from the great work of the Stan team on the "modeling language" side. As a proof of concept I have implemented a plain Hamiltonian Monte Carlo sampler for a random effect logistic regression model (taken from a course on Multilevel Models by Germán Rodríguez), a coupling of that HMC algorithm (as in "Unbiased Hamiltonian Monte Carlo with couplings", see also this very recent article on the topic of coupling HMC), and then upper bounds on the total variation distance between the chain and its limiting distribution, as in "Estimating Convergence of Markov chains with L-Lag Couplings".

This article will discuss how to graph, organize, and set-up data using sklearn, pandas, and NumPy in reference to the Kaggle project. I am going to be using Jupyter Labs, and the code will be based on that. Sklearn: Sklearn is a machine learning software in Python's library. The main features are used for statistical modeling for topics such as regression. The sklearn API can be referenced here.

Empirical risk minimization (ERM) is a principle in statistical learning. Through ERM, we can measure the performance of a family of learning algorithms based on a set of observed training data empirically without knowing the true distribution of the data and derive theoretical bounds on the performance. ERM is routinely applied in a wide range of learning problems such as regression, classification, and clustering. In recent years, with the increasing popularity in privacy-preserving machine learning that satisfies formal privacy guarantees such as differential privacy (DP) [10], the topic of privacy-preserving ERM has also been investigated. Generally speaking, differentially private empirical risk minimization (DP-ERM) can be realized by perturbing the output (estimation or prediction), the objective function (input), or iteratively during the algorithmic optimization, given an ERM problem. For output perturbation, randomization mechanisms need to be applied every time a new output is released; for iterative algorithmic perturbation, each iteration incurs a privacy loss, careful planning and implementation of privacy accounting methods to minimize the overall privacy loss is critical. In this paper, we focus on differentially private perturbation of objective functions. Once an objective function is perturbed, the subsequent optimization does not incur additional privacy loss and all outputs generated from the optimization are also differentially private.

We consider the problem of high-dimensional Ising model selection using neighborhood-based least absolute shrinkage and selection operator (Lasso). It is rigorously proved that under some mild coherence conditions on the population covariance matrix of the Ising model, consistent model selection can be achieved with sample sizes $n=\Omega{(d^3\log{p})}$ for any tree-like graph in the paramagnetic phase, where $p$ is the number of variables and $d$ is the maximum node degree. When the same conditions are imposed directly on the sample covariance matrices, it is shown that a reduced sample size $n=\Omega{(d^2\log{p})}$ suffices. The obtained sufficient conditions for consistent model selection with Lasso are the same in the scaling of the sample complexity as that of $\ell_1$-regularized logistic regression. Given the popularity and efficiency of Lasso, our rigorous analysis provides a theoretical backing for its practical use in Ising model selection.

Figure 1 – Figure supplement 1: Learning curves on the random split-half validation used for model building. To facilitate comparisons, we evaluated predictions of age, fluid intelligence and neuroticism from a complete set of socio-demographic variables without brain imaging using the coefficient of determination R2 metric (y-axis) to compare results obtained from 100 to 3000 training samples (x-axis). The cross-validation (CV) distribution was obtained from 100 Monte Carlo splits. Across targets, performance started to plateau after around 1000 training samples with scores virtually identical to the final model used in subsequent analyses. These benchmarks suggest that inclusion of additional training samples would not have led to substantial improvements in performance.

We propose a nested weighted Tchebycheff Multi-objective Bayesian optimization framework where we build a regression model selection procedure from an ensemble of models, towards better estimation of the uncertain parameters of the weighted-Tchebycheff expensive black-box multi-objective function. In existing work, a weighted Tchebycheff MOBO approach has been demonstrated which attempts to estimate the unknown utopia in formulating acquisition function, through calibration using a priori selected regression model. However, the existing MOBO model lacks flexibility in selecting the appropriate regression models given the guided sampled data and therefore, can under-fit or over-fit as the iterations of the MOBO progress, reducing the overall MOBO performance. As it is too complex to a priori guarantee a best model in general, this motivates us to consider a portfolio of different families of predictive models fitted with current training data, guided by the WTB MOBO; the best model is selected following a user-defined prediction root mean-square-error-based approach. The proposed approach is implemented in optimizing a multi-modal benchmark problem and a thin tube design under constant loading of temperature-pressure, with minimizing the risk of creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff MOBO model performance is compared with different MOBO frameworks with respect to accuracy in parameter estimation, Pareto-optimal solutions and function evaluation cost. This method is generalized enough to consider different families of predictive models in the portfolio for best model selection, where the overall design architecture allows for solving any high-dimensional (multiple functions) complex black-box problems and can be extended to any other global criterion multi-objective optimization methods where prior knowledge of utopia is required.

We show you how one might code their own linear regression module in Python. Linear regression is the simplest machine learning model you can learn, y

We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be prohibitive, and it may be imperative for them to use sparsification techniques. While most existing work on sparsified mean estimation is agnostic to the characteristics of the data vectors, in many practical applications such as federated learning, there may be spatial correlations (similarities in the vectors sent by different nodes) or temporal correlations (similarities in the data sent by a single node over different iterations of the algorithm) in the data vectors. We leverage these correlations by simply modifying the decoding method used by the server to estimate the mean. We provide an analysis of the resulting estimation error as well as experiments for PCA, K-Means and Logistic Regression, which show that our estimators consistently outperform more sophisticated and expensive sparsification methods.

Pyspark is an Apache Spark which is an open-source cluster-computing framework for large-scale data processing written in Scala.