Feb 27, 2023 · Graph of Convex & Non-Convex. Log Loss (or cross entropy loss) is a popular objective function used in Logistic Regression.

The need is for $J(\theta)$ to be convex (as a function of $\theta$), so you need $Cost(h_{\theta}(x), y)$ to be a convex function of $\theta$, not $x$. Note that the function inside the sigmoid is linear in $\theta$.

Feb 25, 2023 · By proving the convexity of the log-loss function, we have shown that the optimization problem in logistic regression is well-posed and can be efficiently solved using standard convex optimization methods.

Dec 31, 2020 · Hypothesis function for logistic regression. The sigmoid function is also referred to as the logistic function. The graph of the sigmoid function look like this:

From Linear to Logistic Regression Can we replace g(x ) by sign(g(x ))? How about a soft-version of sign(g(x ))? This gives a logistic regression. 10/25

A Python script to graph simple cost functions for linear and logistic regression. Showing how choosing convex or con-convex function can effect gradient descent.

To minimize a one-dimensional convex function, we can use bisection. We start with an interval that is guaranteed to contain a minimizer. At each step, depending on the slope of the function at the middle of the interval, we shrink the interval by choosing either the left-or right-sided interval.

In this class, we will see logistic regression, a widely used classification algorithm. Contrary to linear regression, there is no closed-form solution and one needs to solve it thanks to iterative convex optimization algorithms. We will then see the basics of convex analysis.

Logistic regression — a discriminative learning approach that directly models P(y!x) for classification

Oct 14, 2024 · By mastering 3D visualizations of decision boundaries, you’ll gain a deeper understanding of your logistic regression models and make better-informed decisions about model performance and...