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larger training set deviance for smaller values of reg_lambda: bug in convergence criterion? #65

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hugoguh opened this issue May 9, 2016 · 4 comments · May be fixed by #226
Open

larger training set deviance for smaller values of reg_lambda: bug in convergence criterion? #65

hugoguh opened this issue May 9, 2016 · 4 comments · May be fixed by #226
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@hugoguh
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hugoguh commented May 9, 2016 •
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I noticed it while working on cvpyglmnet:

screen shot 2016-05-09 at 2 01 10 pm

If you notice there is a weird behavior on the training performance: the training set deviance is supposed to always go down as reg_lambda approaches zero (or log(Lambda) becomes more negative).

Here’s some code for you to replicate it:
doesn’t happen always, for instance try using np.random.seed(0) 

import numpy as np
import scipy.sparse as sps
from sklearn.preprocessing import StandardScaler
import scikits.bootstrap as boot
from pyglmnet import GLM
np.random.seed(42)

# create an instance of the GLM class
reg_lambda = np.exp(np.linspace(-10, -3, num=100))
model = GLM(distr='poisson', verbose=False, alpha=0.95, reg_lambda=reg_lambda)

n_samples, n_features = 10000, 100

# coefficients
beta0 = np.random.normal(0.0, 1.0, 1)
beta = sps.rand(n_features, 1, 0.1)
beta = np.array(beta.todense())

# training data
Xr = np.random.normal(0.0, 1.0, [n_samples, n_features])
yr = model.simulate(beta0, beta, Xr)

# testing data
Xt = np.random.normal(0.0, 1.0, [n_samples, n_features])
yt = model.simulate(beta0, beta, Xt)

# fit Generalized Linear Model
scaler = StandardScaler().fit(Xr)

fit and compute deviance
using average deviance, just a scaler diference but better measure when cross-validating because different folds might have different number of elements, use the commented line for deviance 

yrhat = model.fit_predict(scaler.transform(Xr), yr)
#dev_t = [model.deviance(yr, i) for i in yrhat]
dev_t = [model.deviance(yr, i)/float(np.shape(yrhat)[1]) for i in yrhat]

now plot

%matplotlib inline
import matplotlib.pyplot as plt
upto = 60
plt.plot(np.log(model.reg_lambda[0:upto]), dev_t[0:upto], '-o', c='k')
plt.xlabel('log(Lambda)')
plt.ylabel('Poisson Deviance')

Here’s the output:
screen shot 2016-05-09 at 1 48 14 pm

play around with the range of reg_lambdas and also try with other random.seed (different simulated Xr and yr).

Any idea on where it is coming from? At first I thought it was a warm start effect but @pavanramkumar says it starts by fitting the larger reg_lambdas.
This might give a hint, it seems to not depend on the actual value of reg_lambda: when it happens it seems to always happen towards the end, see if I use a slightly different range of reg_lambdas when instantiating the model:

reg_lambda = np.exp(np.linspace(-8, -3, num=100))

screen shot 2016-05-09 at 2 03 17 pm
@jasmainak jasmainak added the bug label May 10, 2016
@jasmainak
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The last plot just looks like a zoomed version of the first plot to me. Did you try other metrics like RMSE or so?

@pavanramkumar pavanramkumar changed the title convergence bug? larger training set deviance for smaller values of reg_lambda: bug? May 11, 2016
@pavanramkumar pavanramkumar changed the title larger training set deviance for smaller values of reg_lambda: bug? larger training set deviance for smaller values of reg_lambda: bug in convergence criterion? May 11, 2016
@pavanramkumar
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renaming a few issue titles for clarity

@jasmainak
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I think this is related to #226. You just need to use a smaller learning_rate

@jasmainak jasmainak linked a pull request Nov 9, 2017 that will close this issue
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@jasmainak
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@pavanramkumar @hugoguh this seems to be fixed now with latest code. Just run this:

import numpy as np
import scipy.sparse as sps
from sklearn.preprocessing import StandardScaler
import scikits.bootstrap as boot
from pyglmnet import GLM, simulate_glm
np.random.seed(42)

# create an instance of the GLM class
reg_lambda = np.exp(np.linspace(-10, -3, num=100))

n_samples, n_features = 10000, 100

# coefficients
beta0 = np.random.normal(0.0, 1.0, 1)[0]
beta = sps.rand(n_features, 1, 0.1)
beta = np.array(beta.todense())[:, 0]

# training data
Xr = np.random.normal(0.0, 1.0, [n_samples, n_features])
yr = simulate_glm('poisson', beta0, beta, Xr)

# testing data
Xt = np.random.normal(0.0, 1.0, [n_samples, n_features])
yt = simulate_glm('poisson', beta0, beta, Xt)

# fit Generalized Linear Model
scaler = StandardScaler().fit(Xr)

dev_t = list()
for rl in reg_lambda:
    glm = GLM(distr='poisson', verbose=True, alpha=0.95, reg_lambda=rl)
    glm.fit(scaler.transform(Xr), yr)
    dev_t.append(glm.score(scaler.transform(Xr), yr))


import matplotlib.pyplot as plt
upto = 60
plt.plot(np.log(reg_lambda[0:upto]), dev_t[0:upto], '-o', c='k')
plt.xlabel('log(Lambda)')
plt.ylabel('Poisson Deviance')

I get:

Screen Shot 2020-08-14 at 4 58 26 PM

can you close if you agree?

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[MRG] FIX problem of learning rate jasmainak/pyglmnet
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@pavanramkumar @hugoguh @jasmainak