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 …

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 …

Feb 27, 2023 · Log Loss is a convex function for Logistic Regression because it is a continuous, differentiable, and strictly convex function. This means that it has a unique point of global …

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 …

Oct 5, 2017 · How to prove that logistic loss is a convex function? f(x) = log(1 +e−x)? f (x) = log (1 + e − x)?

We show that Logistic Regression and Softmax are convex. Let X = {~x1, . . . , ~xn}, ~xi ∈ Rd, be a set of examples. Let ~y = {y1, . . . , yn}, yi ∈ {−1, +1}, be a corresponding set of labels. …

Can we replace g(x) by sign(g(x))? How about a soft-version of sign(g(x))? This gives a logistic regression. The rst term is linear, so it is convex. The second term: Gradient: Tx ! Therefore …

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

Jun 12, 2019 · Why does logistic regression with a logarithmic cost function converge to the optimal classification?

May 7, 2025 · For logistic regression, this (cross-entropy) loss function is conveniently convex. A convex function has just one minimum; there are no local minima to get stuck in, so gradient …