bpr_log_likelihood {BPRMeth} | R Documentation

## Compute observation model log-likelihood

### Description

These functions evaluate the model log-likelihood and gradient for different observation models. Available models are "bpr" (i.e. "bernoulli" or "binomial"), "beta" and "lr" (i.e. "gaussian"). There are also functions to compute the sum and weighted sum of the observation model likelihoods, e.g. required for the EM algorithm. These functions are written in C++ for efficiency.

### Usage

    bpr_log_likelihood(w, X, H, lambda, is_nll)

    bpr_gradient(w, X, H, lambda, is_nll)

    betareg_log_likelihood(w, X, H, lambda, is_nll)

    betareg_gradient(w, X, H, lambda, is_nll)

    sum_weighted_bpr_lik(w, X_list, H_list, r_nk, lambda, is_nll)

    sum_weighted_bpr_grad(w, X_list, H_list, r_nk, lambda, is_nll)

    sum_weighted_betareg_lik(w, X_list, H_list, r_nk, lambda, is_nll)

    sum_weighted_betareg_grad(w, X_list, H_list, r_nk, lambda, is_nll)

    lr_log_likelihood(w, X, H, lambda = 0.5, is_nll = FALSE)

### Arguments

`w` | A vector of parameters (i.e. coefficients of the basis functions)
`X` | An `L X C` matrix, where L are the total number of observations. The first column contains the input observations x (i.e. CpG locations). If "binomial" model then C=3, and 2nd and 3rd columns contain total number of trials and number of successes respectively. If "bernoulli" or "gaussian" model, then C=2 containing the output y (e.g. methylation level). if "beta" model, then C=3, where 2nd column contains output y and 3rd column the dispersion parameter. Each row corresponds to each row of the design matrix `H`.
`H` | The `L x M` matrix design matrix, where L is the number of observations and M the number of basis functions.
`lambda` | The complexity penalty coefficient for penalized regression.
`is_nll` | Logical, indicating if the Negative Log Likelihood should be returned.
`X_list` | A list of elements of length N, where each element is an `L x K` matrix of observations X.
`H_list` | A list of elements of length N, where each element contains the `L x M` design matrices `H`.
`r_nk` | A vector of length N containing the posterior probabilities (i.e. responsibilities) for each element of `X_list`.

### Value

Returns the log likelihood or gradient of the observation model.

### Author(s)

C.A.Kapourani C.A.Kapourani@ed.ac.uk

### See Also

`eval_functions`, `infer_profiles_mle`

[Package BPRMeth version 1.12.0 Index]