This course is a lead-in to deep learning and neural networks - it covers a popular and fundamental technique used in machine learning, data science and statistics: logistic regression. We cover the theory from the ground up: derivation of the solution, and applications to real-world problems. We show you how one might code their own logistic regression module in Python. This course does not require any external materials. Everything needed (Python, and some Python libraries) can be obtained for free.

Python is one of the fastest-growing platforms for applied machine learning. In this mini-course, you will discover how you can get started, build accurate models and confidently complete predictive modeling machine learning projects using Python in 14 days. This is a big and important post. You might want to bookmark it. Python Machine Learning Mini-Course Photo by Dave Young, some rights reserved.

Continuous blood pressure (BP) measurements can reflect a body's response to diseases and serve as a predictor of cardiovascular and other health conditions. While current cuff-based BP measurement methods are incapable of providing continuous BP readings, invasive BP monitoring methods also tend to cause patient dissatisfaction and can potentially cause infection. In this research, we developed a method for estimating blood pressure based on the features extracted from Electrocardiogram (ECG) and Photoplethysmogram (PPG) signals and the Arterial Blood Pressure (ABP) data. The vector of features extracted from the preprocessed ECG and PPG signals is used in this approach, which include Pulse Transit Time (PTT), PPG Intensity Ratio (PIR), and Heart Rate (HR), as the input of a clustering algorithm and then developing separate regression models like Random Forest Regression, Gradient Boosting Regression, and Multilayer Perceptron Regression algorithms for each resulting cluster. We evaluated and compared the findings to create the model with the highest accuracy by applying the clustering approach and identifying the optimal number of clusters, and eventually the acceptable prediction model. The paper compares the results obtained with and without this clustering. The results show that the proposed clustering approach helps obtain more accurate estimates of Systolic Blood Pressure (SBP) and Diastolic Blood Pressure (DBP). Given the inconsistency, high dispersion, and multitude of trends in the datasets for different features, using the clustering approach improved the estimation accuracy by 50-60%.

After deploying a clinical prediction model, subsequently collected data can be used to fine-tune its predictions and adapt to temporal shifts. Because model updating carries risks of over-updating/fitting, we study online methods with performance guarantees. We introduce two procedures for continual recalibration or revision of an underlying prediction model: Bayesian logistic regression (BLR) and a Markov variant that explicitly models distribution shifts (MarBLR). We perform empirical evaluation via simulations and a real-world study predicting COPD risk. We derive "Type I and II" regret bounds, which guarantee the procedures are non-inferior to a static model and competitive with an oracle logistic reviser in terms of the average loss. Both procedures consistently outperformed the static model and other online logistic revision methods. In simulations, the average estimated calibration index (aECI) of the original model was 0.828 (95%CI 0.818-0.938). Online recalibration using BLR and MarBLR improved the aECI, attaining 0.265 (95%CI 0.230-0.300) and 0.241 (95%CI 0.216-0.266), respectively. When performing more extensive logistic model revisions, BLR and MarBLR increased the average AUC (aAUC) from 0.767 (95%CI 0.765-0.769) to 0.800 (95%CI 0.798-0.802) and 0.799 (95%CI 0.797-0.801), respectively, in stationary settings and protected against substantial model decay. In the COPD study, BLR and MarBLR dynamically combined the original model with a continually-refitted gradient boosted tree to achieve aAUCs of 0.924 (95%CI 0.913-0.935) and 0.925 (95%CI 0.914-0.935), compared to the static model's aAUC of 0.904 (95%CI 0.892-0.916). Despite its simplicity, BLR is highly competitive with MarBLR. MarBLR outperforms BLR when its prior better reflects the data. BLR and MarBLR can improve the transportability of clinical prediction models and maintain their performance over time.

For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM estimation is potentially very sensitive to outliers. Robustified GMM estimators have been developed in the past, but suffer from several drawbacks: computational intractability, poor dimension-dependence, and no quantitative recovery guarantees in the presence of a constant fraction of outliers. In this work, we develop the first computationally efficient GMM estimator (under intuitive assumptions) that can tolerate a constant $\epsilon$ fraction of adversarially corrupted samples, and that has an $\ell_2$ recovery guarantee of $O(\sqrt{\epsilon})$. To achieve this, we draw upon and extend a recent line of work on algorithmic robust statistics for related but simpler problems such as mean estimation, linear regression and stochastic optimization. As two examples of the generality of our algorithm, we show how our estimation algorithm and assumptions apply to instrumental variables linear and logistic regression. Moreover, we experimentally validate that our estimator outperforms classical IV regression and two-stage Huber regression on synthetic and semi-synthetic datasets with corruption.

Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a simple solution by extending the time-tested iterative reweighted least square (IRLS) in generalised linear regression. We use two sub-networks to parametrise the prediction and uncertainty estimation, enabling easy handling of complex inputs and nonlinear response. The two sub-networks have shared representations and are trained via two complementary loss functions for the prediction and the uncertainty estimates, with interleaving steps as in a cooperative game. Compared with more complex models such as MC-Dropout or SDE-Net, our proposed network is simpler to implement and more robust (insensitive to varying aleatoric and epistemic uncertainty).

Stochastic gradient descent (SGD) has been demonstrated to generalize well in many deep learning applications. In practice, one often runs SGD with a geometrically decaying stepsize, i.e., a constant initial stepsize followed by multiple geometric stepsize decay, and uses the last iterate as the output. This kind of SGD is known to be nearly minimax optimal for classical finite-dimensional linear regression problems (Ge et al., 2019), and provably outperforms SGD with polynomially decaying stepsize in terms of the statistical minimax rates. However, a sharp analysis for the last iterate of SGD with decaying step size in the overparameterized setting is still open. In this paper, we provide problem-dependent analysis on the last iterate risk bounds of SGD with decaying stepsize, for (overparameterized) linear regression problems. In particular, for SGD with geometrically decaying stepsize (or tail geometrically decaying stepsize), we prove nearly matching upper and lower bounds on the excess risk. Our results demonstrate the generalization ability of SGD for a wide class of overparameterized problems, and can recover the minimax optimal results up to logarithmic factors in the classical regime. Moreover, we provide an excess risk lower bound for SGD with polynomially decaying stepsize and illustrate the advantage of geometrically decaying stepsize in an instance-wise manner, which complements the minimax rate comparison made in previous work.

Understanding logistic function is an important prerequisite to understanding logistic regression. So let's start by understanding what logistic function is. Logistic function is a type of sigmoid function that squishes values between 0 and 1. Although sigmoid function is an umbrella term for logistic and other functions, the term is often used to refer to logistic function. For instance, the logistic function is commonly known as sigmoid activation function in the context of neural networks.

Concrete is the most commonly used material in civil engineering. That is why lots of research and experiments are done on concrete. In this experiment, it is tried to understand how the compressive strength will be according to the materials in the concrete. Concrete has many properties like shear strength, tensile strength. Compressive strength is one of the most important properties.

Surface roughness is primary measure of pavement performance that has been associated with ride quality and vehicle operating costs. Of all the surface roughness indicators, the International Roughness Index (IRI) is the most widely used. However, it is costly to measure IRI, and for this reason, certain road classes are excluded from IRI measurements at a network level. Higher levels of distresses are generally associated with higher roughness. However, for a given roughness level, pavement data typically exhibits a great deal of variability in the distress types, density, and severity. It is hypothesized that it is feasible to estimate the IRI of a pavement section given its distress types and their respective densities and severities. To investigate this hypothesis, this paper uses data from in-service pavements and machine learning methods to ascertain the extent to which IRI can be predicted given a set of pavement attributes. The results suggest that machine learning can be used reliably to estimate IRI based on the measured distress types and their respective densities and severities. The analysis also showed that IRI estimated this way depends on the pavement type and functional class. The paper also includes an exploratory section that addresses the reverse situation, that is, estimating the probability of pavement distress type distribution and occurrence severity/extent based on a given roughness level.