# Questions tagged [hessian]

For on-topic questions involving the Hessian matrix, a square matrix generalizing the second derivative. Please include also a statistical methods tag. For purely mathemathical questions about the Hessian it is better to ask on math.SE at https://math.stackexchange.com/.

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### Multiclass: I want to develop a customized objective function with weights given by both label and prediction, for Xgboost

I want to develop a customized objective function with weights given by both label and prediction, for Xgboost. Example, let's say you have 2 classes I want to assign a penalties according to this ...
44 views

### Saddle-free Newton method for SGD - while Newton attracts saddles, is it worth to actively replel them?

While 2nd order methods have many advantages, e.g. natural gradient (e.g. in L-BFGS) attracts to close zero gradient point, which is usually saddle. Other try to pretend that our very non-convex ...
60 views

### How positive definite Hessian approximations for SGD (e.g. Gauss-Newton) handle saddles?

For example due to symmetry of parameters, functions optimized in machine learning usually have huge number of local minima and saddles - growing exponentially with dimension. I am trying to ...
94 views

### Inverting Hessian using Generalized Inverse for Inference

I am estimating a survival model with MLE. I use optim to maximize the likelihood function, and I intend to use the Hessian matrix returned by optim to get the standard errors (which lie on the ...
734 views

### How the Hessian matrix is used in optimization if you can't invert it

I've seen quite a lot of work to do with approximating the Hessian such as the Hessian Vector Product but I'm not entirely sure how knowing the Hessian helps us evaluate the gradient step to take. ...
122 views

### Computing the Hessian Matrix Diagonal of a multi-layered Feed Forward Neural Network

I am working on using a Feedforward multi-layered perceptron as a function approximator for the pressure distribution of a groundwater system. I am essentially trying to solve a boundary value problem ...
89 views

### Should Bayesian estimated error smaller than MLE?

I am dealing with a fitting problem. Specifically, I am fitting a Lorentzian profile to the power spectrum of an solar-like oscillating star. Three parameters in the Lorentzian profile characterize ...
38 views

### Non-linear Likelihood function, large estimated standard errors

I have a highly non-linear (lots of jumps) likelihood function with K parameters (For example, a marked Hawkes Process used in seismology study). I implemented the L-BFGS-B optimization routine and it ...
I have question about the $R\{.\}$ function in Bishop's book on page 254 (see snippet below). My questions are as follows: I assume $R\{\bf w\}$ in (5.97) is the premultiplication of $\bf{v}^{T}$ ...