Likelihood fit

Likelihood fitting of normally distributed samples.

In [ ]:

import numpy as np
import proplot as pplt

from slimfit.symbols import Symbol
from slimfit.models import Model
from slimfit.fit import Fit
from slimfit.functions import gaussian_sympy
from slimfit.loss import LogLoss

import numpy as np import proplot as pplt from slimfit.symbols import Symbol from slimfit.models import Model from slimfit.fit import Fit from slimfit.functions import gaussian_sympy from slimfit.loss import LogLoss

In [ ]:

gt_params = {"mu": 2.4, "sigma": 0.7}

xdata = np.random.normal(gt_params["mu"], scale=gt_params["sigma"], size=500)
model = Model({Symbol("p"): gaussian_sympy(Symbol("x"), Symbol("mu"), Symbol("sigma"))})

gt_params = {"mu": 2.4, "sigma": 0.7} xdata = np.random.normal(gt_params["mu"], scale=gt_params["sigma"], size=500) model = Model({Symbol("p"): gaussian_sympy(Symbol("x"), Symbol("mu"), Symbol("sigma"))})

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parameters = model.define_parameters("mu sigma")

parameters = model.define_parameters("mu sigma")

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fit = Fit(model, parameters, data={"x": xdata}, loss=LogLoss())

# execution time: 12.5ms
likelihood_result = fit.execute()

fit = Fit(model, parameters, data={"x": xdata}, loss=LogLoss()) # execution time: 12.5ms likelihood_result = fit.execute()

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hist, edges = np.histogram(xdata, bins="fd", density=True)
centers = (edges[:-1] + edges[1:]) / 2.0
centers, edges

hist, edges = np.histogram(xdata, bins="fd", density=True) centers = (edges[:-1] + edges[1:]) / 2.0 centers, edges

In [ ]:

fig, ax = pplt.subplots()
ax.scatter(centers, hist, color="r")
ax.hist(xdata, bins="fd", density=True, color="gray")
pplt.show()

fig, ax = pplt.subplots() ax.scatter(centers, hist, color="r") ax.hist(xdata, bins="fd", density=True, color="gray") pplt.show()

In [ ]:

fit = Fit(model, parameters, data={"x": centers, "p": hist})
binned_lsq_result = fit.execute()
print(binned_lsq_result)

fit = Fit(model, parameters, data={"x": centers, "p": hist}) binned_lsq_result = fit.execute() print(binned_lsq_result)

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binned_lsq_result.guess

binned_lsq_result.guess

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print(likelihood_result.hessian)
print(binned_lsq_result.hessian)

print(likelihood_result.hessian) print(binned_lsq_result.hessian)

In [ ]:

data = {"x": np.linspace(0.0, 5.0, num=100)}

fig, ax = pplt.subplots()
ax.plot(data["x"], model(**gt_params, **data)["p"], color="r")
ax.plot(
    data["x"],
    model(**likelihood_result.parameters, **data)["p"],
    linestyle="--",
    color="k",
    label="likelihood",
)
ax.plot(
    data["x"],
    model(**binned_lsq_result.parameters, **data)["p"],
    linestyle="--",
    color="b",
    label="lsq",
)

ax.hist(xdata, bins="fd", density=True, color="grey", zorder=-1)
ax.scatter(centers, hist, color="b", marker="x")
ax.format(xlabel="x", ylabel="p(x)", title="Gaussian Fit")
ax.legend(loc="t")
pplt.show()

data = {"x": np.linspace(0.0, 5.0, num=100)} fig, ax = pplt.subplots() ax.plot(data["x"], model(**gt_params, **data)["p"], color="r") ax.plot( data["x"], model(**likelihood_result.parameters, **data)["p"], linestyle="--", color="k", label="likelihood", ) ax.plot( data["x"], model(**binned_lsq_result.parameters, **data)["p"], linestyle="--", color="b", label="lsq", ) ax.hist(xdata, bins="fd", density=True, color="grey", zorder=-1) ax.scatter(centers, hist, color="b", marker="x") ax.format(xlabel="x", ylabel="p(x)", title="Gaussian Fit") ax.legend(loc="t") pplt.show()