A treatment regime is a rule that assigns a treatment to patients based on their covariate information. Recently, estimation of the optimal treatment regime that yields the greatest overall expected clinical outcome of interest has attracted a lot of attention. In this work, we consider estimation of the optimal treatment regime with electronic medical record data under a semi-supervised setting. Here, data consist of two parts: a set of `labeled' patients for whom we have the covariate, treatment and outcome information, and a much larger set of `unlabeled' patients for whom we only have the covariate information. We proposes an imputation-based semi-supervised method, utilizing `unlabeled' individuals to obtain a more efficient estimator of the optimal treatment regime. The asymptotic properties of the proposed estimators and their associated inference procedure are provided. Simulation studies are conducted to assess the empirical performance of the proposed method and to compare with a fully supervised method using only the labeled data. An application to an electronic medical record data set on the treatment of hypotensive episodes during intensive care unit (ICU) stays is also given for further illustration.

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Regression-based machine learning models are used to predict the value of a continuous attribute. As with all supervised machine learning problems the model is trained using a set of features (X) to learn the mapping to a target variable (y). In the case of regression, the target is a continuous variable such as the price of a house. Probably the simplest regression algorithm is linear regression. Simple linear regression, where there is only one feature and one target, is represented by the equation shown below.

We propose the Factor Augmented sparse linear Regression Model (FARM) that not only encompasses both the latent factor regression and sparse linear regression as special cases but also bridges dimension reduction and sparse regression together. We provide theoretical guarantees for the estimation of our model under the existence of sub-Gaussian and heavy-tailed noises (with bounded (1+x)-th moment, for all x>0), respectively. In addition, the existing works on supervised learning often assume the latent factor regression or the sparse linear regression is the true underlying model without justifying its adequacy. To fill in such an important gap, we also leverage our model as the alternative model to test the sufficiency of the latent factor regression and the sparse linear regression models. To accomplish these goals, we propose the Factor-Adjusted de-Biased Test (FabTest) and a two-stage ANOVA type test respectively. We also conduct large-scale numerical experiments including both synthetic and FRED macroeconomics data to corroborate the theoretical properties of our methods. Numerical results illustrate the robustness and effectiveness of our model against latent factor regression and sparse linear regression models.

Traditional methods for matching in causal inference are impractical for high-dimensional datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact matching find exponentially fewer matches as the input dimension grows, and propensity score matching may match highly unrelated units together. To overcome this problem, we develop theoretical results which motivate the use of neural networks to obtain non-trivial, multivariate balancing scores of a chosen level of coarseness, in contrast to the classical, scalar propensity score. We leverage these balancing scores to perform matching for high-dimensional causal inference and call this procedure neural score matching. We show that our method is competitive against other matching approaches on semi-synthetic high-dimensional datasets, both in terms of treatment effect estimation and reducing imbalance.

Welcome Hi again, hi again! If you've been catching up with my blog, thanks for your continuous support If you're new here, thank you for giving my blog a chance Since I started learning R, I've thought about making code comparisons between Python and R. Concidentally, I've also started learning machine learning so I thought... why not try and compare machine learning codes between Python and R! So far, I've learned how to build logistic regression models using Python and R. Project 8 is divided into parts 1 and 2 where the codes using Python and R will be described respectively. I will be using the Iris dataset to demonstrate how the codes work If you're someone who requires assistive software to read, I suggest downloading the PDF documents to read the codes. Python - Jupyter Notebook For this project, I built a logistic regression model using sklearn. For starters, the packages I used were Pandas, Numpy, Scipy, Sklearn, and matplotlib.

The all-possible-regressions procedure considers all possible subsets of the pool of potential explanatory variables Xi (with i 1, 2, …, m). It then identifies a small group of regression models which are "good" according to a specified criterion. A detailed examination of these models can lead to the selection of the final model. If there are m candidate explanatory variables: 2 m regressions for all possible subsets (e.g. if m 10, then there are 1024 possible regression models) The function leaps() (from package leaps) performs an exhaustive search for the best subsets of the explanatory variables for predicting the response variable in linear regression. This gave us a little idea but still, we are not sure how many parameters to be used.

Hyperparameters are those parameters in Machine learning algorithms that are used to control the learning process of algorithms. Hyperparameter tuning is the process of finding the best hyperparameters which help us to build more accurate machine learning models. Note: There is a difference between Model Parameters and Hyper Parameters. Model parameters are learned from data e.g. Slope and intercept in Linear Regression models, and Hyperparameters are those which we set such as L1 or L2 Regularization in Regression Model.

We develop a mixtures-of-experts (ME) approach to the multiclass classification where the predictors are univariate functions. It consists of a ME model in which both the gating network and the experts network are constructed upon multinomial logistic activation functions with functional inputs. We perform a regularized maximum likelihood estimation in which the coefficient functions enjoy interpretable sparsity constraints on targeted derivatives. We develop an EM-Lasso like algorithm to compute the regularized MLE and evaluate the proposed approach on simulated and real data.

A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables). Multiple linear regression (MLR), also known simply as multiple regression, is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. Multiple regression is an extension of linear (OLS) regression that uses just one explanatory variable. Let's try to predict of startups using Multiple Linear Regression in Python We will be using Scikit-learn Library to import the necessary functions required for this Exercise. We will be using Pandas and Numpy for Data Exploration.