In this section, we will try to implement a very simple example of logisitic regression. For this example, we will try to predict the result(pass/fail) of a student based on his 2 test scores. Notice that the predicted result is a value between 0 and 1, it can be interpreted as the probability that the result is a positive (y 1). In our example, for test scores 60 and 75, there is a 87% probability that the student passes. An additional condition like the following can be used inside the predict function for binary output.

In the last section, we saw that linear regression hypothesis function needed to be modified inorder to be used for logistic regression problems. Now the obvious question is whether the same cost function can be used here also or is some modification necessary required. The reason that cost function worked for linear regression was because the hypothesis was linear and hence the cost function was convex shaped with a single global minimum. In case of logistic regression, the hypothesis function is no longer linear because of the sigmoid function and using the same definition for cost function would yield a function as shown below. It will be an impossible task to optimize the parameters theta when using such a cost function with so many local minimums.

The second type of Supervised learning algorithm we will look into is called the Logistic Regression. First things first, it is not a regression algorithm as its name suggests, rather it's used classification purposes. But the name comes from the fact that classification is done by considering the linear regression model. As mentioned earlier, Classification methods are used in problems where we want to label or categorize inputs. In this section we will be dealing with binary classification problems (those with 2 possible outcomes).

The second type of Supervised learning algorithm we will look into is called the Logistic Regression. First things first, it is not a regression algorithm as its name suggests, rather it's used classification purposes. But the name comes from the fact that classification is done by considering the linear regression model. As mentioned earlier, Classification methods are used in problems where we want to label or categorize inputs. In this section we will be dealing with binary classification problems (those with 2 possible outcomes).

Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of counts in a regression context using distributions such as the Poisson and negative binomial. When counts contain only relative information, multinomial or Dirichlet-multinomial models can be more appropriate. We review some of the fundamental connections between multinomial and count models from probability theory, providing detailed proofs. These relationships are useful for methods development in applications such as topic modeling of text data and genomics.

Shiller's CAPE ratio is a popular and useful metric for measuring whether stock prices are overvalued or undervalued relative to earnings. Recently, Vanguard analysts Haifeng Wang, Harshdeep Singh Ahluwalia, Roger A. Aliaga-Díaz, and Joseph H. Davis have written a very interesting paper on forecasting equity returns using Shiller's CAPE and machine learning: "The Best of Both Worlds: Forecasting US Equity Market Returns using a Hybrid Machine Learning – Time Series Approach". First, what is the Shiller CAPE ratio? 1 If we do a simple regression of Shiller's CAPE ratio against future 10-year returns, we observe a very strong relationship. Here we see a historical chart of actual 10-year annualized stock returns vs. those predicted by Shiller's CAPE. Using the Shiller regression, the current CAPE of about 30 suggests near-zero real return over the next 10 years.

Shiller's CAPE ratio is a popular and useful metric for measuring whether stock prices are overvalued or undervalued relative to earnings. Recently, Vanguard analysts Haifeng Wang, Harshdeep Singh Ahluwalia, Roger A. Aliaga-Díaz, and Joseph H. Davis have written a very interesting paper on forecasting equity returns using Shiller's CAPE and machine learning: "The Best of Both Worlds: Forecasting US Equity Market Returns using a Hybrid Machine Learning – Time Series Approach". First, what is the Shiller CAPE ratio? 1 If we do a simple regression of Shiller's CAPE ratio against future 10-year returns, we observe a very strong relationship. Here we see a historical chart of actual 10-year annualized stock returns vs. those predicted by Shiller's CAPE. Using the Shiller regression, the current CAPE of about 30 suggests near-zero real return over the next 10 years.

Random forests are powerful non-parametric regression method but are severely limited in their usage in the presence of randomly censored observations, and naively applied can exhibit poor predictive performance due to the incurred biases. Based on a local adaptive representation of random forests, we develop its regression adjustment for randomly censored regression quantile models. Regression adjustment is based on a new estimating equation that adapts to censoring and leads to quantile score whenever the data do not exhibit censoring. The proposed procedure named {\it censored quantile regression forest}, allows us to estimate quantiles of time-to-event without any parametric modeling assumption. We establish its consistency under mild model specifications. Numerical studies showcase a clear advantage of the proposed procedure.

Supervised learning models, also known as quantitative structure-activity regression (QSAR) models, are increasingly used in assisting the process of preclinical, small molecule drug discovery. The models are trained on data consisting of a finite dimensional representation of molecular structures and their corresponding target specific activities. These models can then be used to predict the activity of previously unmeasured novel compounds. In this work we address two problems related to this approach. The first is to estimate the extent to which the quality of the model predictions degrades for compounds very different from the compounds in the training data. The second is to adjust for the screening dependent selection bias inherent in many training data sets. In the most extreme cases, only compounds which pass an activity-dependent screening are reported. By using a semi-supervised learning framework, we show that it is possible to make predictions which take into account the similarity of the testing compounds to those in the training data and adjust for the reporting selection bias. We illustrate this approach using publicly available structure-activity data on a large set of compounds reported by GlaxoSmithKline (the Tres Cantos AntiMalarial Set) to inhibit in vitro P. falciparum growth.

In this paper, we proposed a novel automated model, called Vulnerability Index for Population at Risk (VIPAR) scores, to identify rare populations for their future shooting victimizations. Likewise, the focused deterrence approach identifies vulnerable individuals and offers certain types of treatments (e.g., outreach services) to prevent violence in communities. The proposed rule-based engine model is the first AI-based model for victim prediction. This paper aims to compare the list of focused deterrence strategy with the VIPAR score list regarding their predictive power for the future shooting victimizations. Drawing on the criminological studies, the model uses age, past criminal history, and peer influence as the main predictors of future violence. Social network analysis is employed to measure the influence of peers on the outcome variable. The model also uses logistic regression analysis to verify the variable selections. Our empirical results show that VIPAR scores predict 25.8% of future shooting victims and 32.2% of future shooting suspects, whereas focused deterrence list predicts 13% of future shooting victims and 9.4% of future shooting suspects. The model outperforms the intelligence list of focused deterrence policies in predicting the future fatal and non-fatal shootings. Furthermore, we discuss the concerns about the presumption of innocence right.