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gradient_descent.py
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gradient_descent.py
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import numpy as np
from bokeh.io import curdoc
from bokeh.layouts import column, row
from bokeh.models import ColumnDataSource, Slider, Button, Toggle, glyphs
from bokeh.plotting import figure
import utils
# Initializations
np.random.seed(40)
num_points = 100
m = 3.1415
x_line = np.arange(-1, 5.1, 0.1)
x = np.random.rand(num_points) * 5
y = m * x + np.random.randn(num_points) * 2
y_line = m * x_line
scatter_data = ColumnDataSource(data=dict(x=x, y=y))
line_data = ColumnDataSource(data=dict(x=x_line, y=y_line))
indexes = np.random.randint(num_points, size=(5,))
start_m = 0
end_m = 6
# Plot scatter plot
pair_plot = figure(
plot_height=400,
plot_width=400,
title="Linear Regression",
tools="crosshair,pan,reset,save,wheel_zoom",
x_range=[-1, 5.5],
y_range=[-4, 20],
)
pair_plot.circle('x', 'y', source=scatter_data, color='blue')
pair_plot.line('x', 'y', source=line_data, color='red')
axis_source = ColumnDataSource(data=dict(
xs=[[-1., 6.], [0., 0.]],
ys=[[0., 0.], [-4., 20]],
))
axis_line = glyphs.MultiLine(
xs='xs', ys='ys', line_color='black',
)
pair_plot.add_glyph(axis_source, axis_line)
line_x = [[i, i] for i in scatter_data.data['x']]
line_y = [
[j, m * scatter_data.data['x'][i]]
for i, j in enumerate(scatter_data.data['y'])
]
error_points = ColumnDataSource(data=dict(x=line_x, y=line_y))
error_glyph = glyphs.MultiLine(
xs='x', ys='y', line_color='green', line_dash='dashed', line_alpha=0.0,
)
pair_plot.add_glyph(error_points, error_glyph)
# Plot error landscape
error_plot = figure(
plot_height=400,
plot_width=400,
title="Error Plots",
tools="crosshair,pan,reset,save,wheel_zoom",
x_range=[start_m - 0.5, end_m + 0.5],
y_range=[0, 2000],
)
error_land_data = ColumnDataSource(data=dict(
x=[m], y=[utils.compute_error(x, y, m)],
))
error_plot.line('x', 'y', source=error_land_data, color='red')
# Set up widgets
set_m = Slider(title='m', value=m, start=start_m, step=0.1, end=end_m)
animate_button = Button(label='► Play', button_type='primary')
cluttered_button = Toggle(
label='Filter points', button_type='primary', width=200
)
button_draw_error = Toggle(
label='Draw Errors', button_type='primary', width=200
)
reset_button = Button(label='Reset errors')
# Setup callbacks
def change_m(attr, old, new):
new_m = set_m.value
x_line = np.arange(-1, 5.1, 0.1)
y_line = new_m * x_line
line_data.data = dict(x=x_line, y=y_line)
if cluttered_button.active:
new_x = x[indexes]
new_y = y[indexes]
else:
new_x = x
new_y = y
new_y_line = set_m.value * new_x
new_line_x = [[i, i] for i in new_x]
new_line_y = [[j, new_y_line[i]] for i, j in enumerate(new_y)]
error_points.data = dict(x=new_line_x, y=new_line_y)
error_param = np.append(error_land_data.data['x'], new_m)
error_val = np.append(
error_land_data.data['y'], utils.compute_error(new_x, new_y, new_m),
)
sort_index = np.argsort(error_param)
error_param = error_param[sort_index]
error_val = error_val[sort_index]
error_land_data.data = dict(x=error_param, y=error_val)
set_m.on_change('value', change_m)
# Animate
def animate_update():
new_m = set_m.value + .1
if new_m > set_m.end:
new_m = 0
set_m.value = new_m
def animate_button_callback():
global callback_id
if animate_button.label == '► Play':
animate_button.label = '❚❚ Pause'
set_m.value = 0
error_land_data.data = {'x': [], 'y': []}
callback_id = curdoc().add_periodic_callback(animate_update, 50)
else:
animate_button.label = '► Play'
curdoc().remove_periodic_callback(callback_id)
animate_button.on_click(animate_button_callback)
# Clutter button
def clutter_button_callback(attr):
if cluttered_button.active:
cluttered_button.button_type = 'success'
scatter_data.data = {'x': x[indexes], 'y': y[indexes]}
new_x = x[indexes]
new_y = y[indexes]
new_y_line = set_m.value * new_x
new_line_x = [[i, i] for i in new_x]
new_line_y = [[j, new_y_line[i]] for i, j in enumerate(new_y)]
error_points.data = dict(x=new_line_x, y=new_line_y)
error_param = error_land_data.data['x']
error_val = [utils.compute_error(new_x, new_y, i) for i in error_param]
error_land_data.data = dict(x=error_param, y=error_val)
error_plot.y_range.update(start=0, end=400)
else:
cluttered_button.button_type = 'primary'
scatter_data.data = {'x': x, 'y': y}
error_param = error_land_data.data['x']
error_val = [utils.compute_error(x, y, i) for i in error_param]
error_land_data.data = dict(x=error_param, y=error_val)
error_plot.y_range.update(start=0, end=2000)
cluttered_button.on_click(clutter_button_callback)
def button_draw_error_callback(attr):
if button_draw_error.active:
button_draw_error.button_type = 'success'
error_glyph.line_alpha = 1.0
error_glyph.line_alpha = 1.0
else:
button_draw_error.button_type = 'primary'
error_glyph.line_alpha = 0.0
error_glyph.line_alpha = 0.0
button_draw_error.on_click(button_draw_error_callback)
button_row = row(cluttered_button, button_draw_error)
plots = row(pair_plot, error_plot)
layout = column(animate_button, set_m, plots, button_row)
curdoc().add_root(layout)
curdoc().title = "LR"