What Happens If You Have Too Much Training Data And Not Enough Testing Data Machine Learning
To give a simple illustration of how bad overfitting can be, consider the example of plumbing equipment (training) a polynomial of social club equal to the number of points of data y'all have. In this case I've generated information with a slope and some unremarkably distributed random dissonance added. If you test it with exactly the same 10 & y values that yous used to generate the polynomial fit by looking at the residuals, all yous see is the numerical error, and you might naively say information technology's a good fit, or at least better than the linear fit (plotted in green) which has much larger residuals. If you plot the bodily polynomial you get (in ruddy), you'll probably run into that information technology really does a terrible job of interpolating between this test data (since we know that the underlying process is simply a straight line), like so:
If you generate a new set of data with the aforementioned ten-values, you lot see that besides as declining at interpolating, this performs about the aforementioned as the linear fit in terms of residuals:
And perhaps worst of all, it fails spectacularly when attempting to extrapolate as the polynomial predictably blows upwards in both directions:
So if "prediction" for your model is interpolating, then overfitting makes information technology bad at that and won't be detected unless you test information technology on not-grooming data. If prediction is extrapolating, so most likely it's fifty-fifty worse at that than it is at interpolating, and again yous won't be able to tell unless yous test information technology on the correct kind of data.
Python code used to generate these plots:
import numpy as np import matplotlib.pyplot equally plt np.random.seed(0) nSamples = 15 slope = ten xvals = np.arange(nSamples) yvals = gradient*xvals + np.random.normal(scale=gradient/x.0, size=nSamples) plt.figure(1) plt.clf() plt.subplot(211) plt.championship('"Perfect" polynomial fit') plt.plot(xvals, yvals, '.', markersize=10) polyCoeffs = np.polyfit(xvals, yvals, nSamples-1) poly_model = np.poly1d(polyCoeffs) linearCoeffs = np.polyfit(xvals, yvals, one) linear_model = np.poly1d(linearCoeffs) xfit = np.linspace(0, nSamples-ane, num=nSamples*l) #yfit_dense = poly_model(xfit) plt.plot(xfit, poly_model(xfit), 'r') plt.plot(xfit, linear_model(xfit), 'grand') plt.subplot(212) plt.plot(xvals, poly_model(xvals) - yvals, 'r.') plt.plot(xvals, linear_model(xvals) - yvals, 'g.') plt.title('Fit residuals for training data (nonzero only due to numerical fault)') #%% Testing interpolation plt.figure(ii) plt.clf() test_yvals = slope*xvals + np.random.normal(scale=slope, size=nSamples) plt.subplot(211) plt.championship('Testing "perfect" polynomial fit with new samples') plt.plot(xvals, test_yvals, '.', markersize=ten) plt.plot(xfit, poly_model(xfit), 'r') plt.plot(xfit, linear_model(xfit), 'm') plt.subplot(212) plt.title('Fit residuals for test data') plt.plot(xvals, poly_model(xvals) - test_yvals, 'r.') plt.plot(xvals, linear_model(xvals) - test_yvals, 'g.') #%% Testing extrapolation extrap_xmin = -5 extrap_xmax = nSamples + 5 xvals_extrap = np.arange(extrap_xmin, extrap_xmax) yvals_extrap = slope*xvals_extrap + np.random.normal(scale=slope, size=len(xvals_extrap)) plt.figure(3) plt.clf() plt.subplot(211) plt.title('Testing "perfect" polynomial fit extrapolation') plt.plot(xvals_extrap, yvals_extrap, '.', markersize=ten) plt.plot(xvals_extrap, poly_model(xvals_extrap), 'r') plt.plot(xvals_extrap, linear_model(xvals_extrap), 'k') plt.subplot(212) plt.title('Fit residuals for extrapolation') plt.plot(xvals_extrap, poly_model(xvals_extrap) - yvals_extrap, 'r.') plt.plot(xvals_extrap, linear_model(xvals_extrap) - yvals_extrap, 'g.') 
What Happens If You Have Too Much Training Data And Not Enough Testing Data Machine Learning,
Source: https://datascience.stackexchange.com/questions/86632/why-is-it-wrong-to-train-and-test-a-model-on-the-same-dataset
Posted by: mosleythouldre.blogspot.com
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