In this work, we consider to improve the model estimation efficiency by aggregating the neighbors' information as well as identify the subgroup membership for each node in the network. A tree-based $l_1$ penalty is proposed to save the computation and communication cost. We design a decentralized generalized alternating direction method of multiplier algorithm for solving the objective function in parallel. The theoretical properties are derived to guarantee both the model consistency and the algorithm convergence. Thorough numerical experiments are also conducted to back up our theory, which also show that our approach outperforms in the aspects of the estimation accuracy, computation speed and communication cost.

Complex phenomena are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to use an approximate likelihood or faster emulator model for efficient statistical inference. We describe a new two-sample testing framework for quantifying the quality of the fit to simulations at fixed parameter values. This framework can leverage any regression method to handle complex high-dimensional data and attain higher power in settings where well-known distance-based tests would not. We also introduce a statistically rigorous test for assessing global goodness-of-fit across simulation parameters. In cases where the fit is inadequate, our method provides valuable diagnostics by allowing one to identify regions in both feature and parameter space which the model fails to reproduce well. We provide both theoretical results and examples which illustrate the effectiveness of our approach.

We are interested in parallelizing the Least Angle Regression (LARS) algorithm for fitting linear regression models to high-dimensional data. We consider two parallel and communication avoiding versions of the basic LARS algorithm. The two algorithms apply to data that have different layout patterns (one is appropriate for row-partitioned data, and the other is appropriate for column-partitioned data), and they have different asymptotic costs and practical performance. The first is bLARS, a block version of LARS algorithm where we update b columns at each iteration. Assuming that the data are row-partitioned, bLARS reduces the number of arithmetic operations, latency, and bandwidth by a factor of b. The second is Tournament-bLARS (T-bLARS), a tournament version of LARS, in which case processors compete, by running several LARS computations in parallel, to choose b new columns to be added into the solution. Assuming that the data are column-partitioned, T-bLARS reduces latency by a factor of b. Similarly to LARS, our proposed methods generate a sequence of linear models. We present extensive numerical experiments that illustrate speed-ups up to 25x compared to LARS.

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.

Continuing my series on the UCI Heart Disease Data, is a tutorial on how to transform a logistic regression into a human transformable test. The tutorial can be found here. I talk about what logistic regression is, in addition to how to use it to make predictions.

A decision tree is a supervised machine learning model used to predict a target by learning decision rules from features. As the name suggests, we can think of this model as breaking down our data by making a decision based on asking a series of questions. Let's consider the following example in which we use a decision tree to decide upon an activity on a particular day: Based on the features in our training set, the decision tree model learns a series of questions to infer the class labels of the samples. As we can see, decision trees are attractive models if we care about interpretability. Although the preceding figure illustrates the concept of a decision tree based on categorical targets (classification), the same concept applies if our targets are real numbers (regression).

Logistic regression is a traditional statistics technique that is also very popular as a machine learning tool. In this StatQuest, I go over the main ideas so that you can understand what it is and how it is used.

Personalized medicine seeks to identify the causal effect of treatment for a particular patient as opposed to a clinical population at large. Most investigators estimate such personalized treatment effects by regressing the outcome of a randomized clinical trial (RCT) on patient covariates. The realized value of the outcome may however lie far from the conditional expectation. We therefore introduce a method called Dirac Delta Regression (DDR) that estimates the entire conditional density from RCT data in order to visualize the probabilities across all possible treatment outcomes. DDR transforms the outcome into a set of asymptotically Dirac delta distributions and then estimates the density using non-linear regression. The algorithm can identify significant patient-specific treatment effects even when no population level effect exists. Moreover, DDR outperforms state-of-the-art algorithms in conditional density estimation on average regardless of the need for causal inference.

We consider off-policy evaluation and optimization with continuous action spaces. We focus on observational data where the data collection policy is unknown and needs to be estimated. We take a semi-parametric approach where the value function takes a known parametric form in the treatment, but we are agnostic on how it depends on the observed contexts. We propose a doubly robust off-policy estimate for this setting and show that off-policy optimization based on this estimate is robust to estimation errors of the policy function or the regression model. Our results also apply if the model does not satisfy our semi-parametric form, but rather we measure regret in terms of the best projection of the true value function to this functional space. Our work extends prior approaches of policy optimization from observational data that only considered discrete actions. We provide an experimental evaluation of our method in a synthetic data example motivated by optimal personalized pricing and costly resource allocation.

As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and mixture correntropy, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multi-kernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum multi-kernel correntropy criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum mixture correntropy criterion (MMCC).