query: Is the log loss function $f(w) = y_t \log(y_p) + (1 - y_t) \log(1 - y_p)$ convex in $w$?
positive_passages.docid: 24230
positive_passages.text: Proof that CRF models and logistic models are convex functions
negative_passages.docid: 19658
negative_passages.text: $\max_{t\in[0,T]}|x(t)|^2 \le |x(0)|^2e^{\int_0^T|y|^2\,\mathrm ds}.$ using gronwall's lemma?
negative_passages.docid: 42302
negative_passages.text: Use of Holder inequality in gradient estimate for harmonic function.
negative_passages.docid: 73074
negative_passages.text: $f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
negative_passages.docid: 109097
negative_passages.text: Is there a unique saddle value for a convex/concave optimization?
negative_passages.docid: 124953
negative_passages.text: A loss and gain problem
negative_passages.docid: 82198
negative_passages.text: Proving Convexity of Multivariate Function using Conditional Univariate Convexity
negative_passages.docid: 150727
negative_passages.text: Characterization convex function.
negative_passages.docid: 13412
negative_passages.text: Motivating sigmoid output units in neural networks starting with unnormalized log probabilities linear in $z=w^Th+b$ and $\phi(z)$
negative_passages.docid: 50113
negative_passages.text: Interpretation of log(1 + x) transformed predictor
negative_passages.docid: 86643
negative_passages.text: Convex function almost surely differentiable.
negative_passages.docid: 142922
negative_passages.text: How to prove that $e^x$ is convex?
negative_passages.docid: 42366
negative_passages.text: Prove $\mathbb{P}(\sup_{t \geq 0} M_t > x \mid \mathcal{F}_0)= 1 \wedge \frac{M_0}{x}$ for a martingale $(M_t)_{t \geq 0}$
negative_passages.docid: 115495
negative_passages.text: Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
negative_passages.docid: 78166
negative_passages.text: Inverse function for a non-decreasing CDF
negative_passages.docid: 72361
negative_passages.text: What is the connection between regularization and the method of lagrange multipliers ?
negative_passages.docid: 102350
negative_passages.text: Cost function of neural network is non-convex?