como-ebnm 0.0.1

Covariate moderated EBNM

como (Covariate moderated EBNM)

Python implimentation of various covariate moderated EBNM

Problem set-up

$$ \begin{align} \hat\beta \sim N(\beta, s^2) \ \beta \sim \pi_0(x) f_0 + \pi_1(x) f_1 \ \log \frac{\pi_1(x)}{\pi_0(x)} = {\bf \beta}^T {\bf x} \end{align} $$

1. A logistic regression model $\log \frac{\pi_1({\bf x})}{\pi_0({\bf x})} = {\bf b}^T {\bf x}$
2. A null component distribution $f_0$
3. A alternative component distribution $f_1$

TwoComponentCoMo

TwoComponentCoMo is an abstract class that encapsulates the logic for fitting two component covariate moderated EBNM. It's constructor requires a dictionary

1. data a dictionary
2. f0 and f1 two ComponentDistribution object (described below)
3. logreg a LogisticRegression object (described below)

ComponentDistribution

We've implmented a few options for $f_0$ and $f_1$ that can be flexibly recombined. ComponentDistribution

1. convolved_log_pdf(self, beta, se): compute $\log p(\hat\beta | s^2) = \log \int N(\hat\beta | \beta, s^2) f(\beta) d\beta$
2. update(self, data): update the parameters of ComponentDistribution using data. Importantly, in practice this function should weight our observations according to the assignment probabilities.

So far we've implimented the following component distributions:

1. PointMassComponent: a point mass, usual choice for $f_0$
2. NormalFixedLocComponent: a normal distribution with fixed location parameter (default loc=0)-- we estimate the scale parameter
3. UnimodalNormalMixtureComponent: a scale mixture of normals, we estimate the mixture distribution $\pi$

LogisticRegression

LogisticRegression.predict(): return (expected) predicted log odds given current parameter estimates LogisticRegression.evidence(): compute the log likelihood or lower bound for current parameter estimates LogisticRegression.update(): update the logistic regression, accounting for the current assignment probabilities

So far we've implimented the following classes inheriting LogisticRegression:

1. LogisticSuSiE: log odds are modeled with a sparse regression $\beta^T x$ where $\beta$ has the sum of single effects prior.
2. InterceptOnly: ignore the covariates, just estimate a constant mixture proprotion for all observations

Putting it all together

We can easily specify a new two component model, inheriting from the base TwoComponentCoMo class

class PointNormalSuSiE(TwoComponentCoMo):
    def __init__(self, data, scale=1.0):
        """
        Initialize Point Normal SuSiE
        (Covariatiate EBNM with "point-normal" effects,
        and SuSiE prior on the mixture proportion)

        Parameters:
            data: dictionary with keys
                'beta' and 'se' for observations and standard errors,
                'X' and 'Z' for annotations and (fixed) covariates resp.
            scale: (initial) scale parameter for the normal mixture component
        """
        f0 = PointMassComponent(0.0)
        f1 = NormalFixedLocComponent(0, scale)
        
        # TODO: make sure `y` is a key in data, otherwise make it
        logreg = LogisticSusie(data, L=10)
        super().__init__(data, f0, f1, logreg)