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Description:

1. Random Data Generator

Name: NYCU Homework 3 Solved
SKU: 89129
Price: 30.00 USD
Availability: InStock

You have to handcraft your geneartor based on one of the approaches given in the

Sequential estimate the mean and variance

Data is given from the univariate gaussian data generator (1.a).Input: as in (1.a) Function:

Call (1.a) to get a new data point from

Use sequential estimation to find the current estimates to and

Input

The precision (i.e., b) for initial prior

All other required inputs for the polynomial basis linear model geneartor (1.b) Function

Call (1.b) to generate one data point

Update the prior, and calculate the parameters of predictive distribution Repeat steps above until the posterior probability converges.

Output

Print the new data point and the current paramters for posterior and predictive distribution.

After probability converged, do the visualization

Ground truth function (from linear model generator)

Final predict result

At the time that have seen 10 data points

At the time that have seen 50 data points

Except ground truth, you have to draw those data points which you have seen before

Draw a black line to represent the mean of function at each point

Draw two red lines to represent the variance of function at each point

In other words, distance between red line and mean is ONE variance

Hint: Online learning

Sample input & output (for reference only)

30 31 Predictive distribution ~ N(0.06869, 1.66008) 32 33 Add data point (-0.19330, 0.24507): 34 35 Postirior mean: 36 0.5760972313 37 0.2450231522 38 -0.0801842453 39 0.0504992402 40 41 Posterior variance:
42 0.2867129751, 0.1311255325, -0.0767580827, 0.0438488542
43 0.1311255325, 0.7892001707, 0.1242887609, -0.0801412282
44 -0.0767580827, 0.1242887609, 0.9176812972, 0.0541575540 45 0.0438488542, -0.0801412282, 0.0541575540, 0.9642058389 46 47 Predictive distribution ~ N(0.62305, 1.34848) 48 49 50 … 51 52 53 Add data point (-0.76990, -0.34768): 54 55 Postirior mean: 56 0.9107496675 57 1.9265499885 58 3.1119297129 59 4.1312375189 60 61 Posterior variance:
62 0.0051883836, -0.0004416700, -0.0086000319, 0.0008247001
63 -0.0004416700, 0.0401966605, 0.0012708906, -0.0554822477 64 -0.0086000319, 0.0012708906, 0.0265353911, -0.0031205875 65 0.0008247001, -0.0554822477, -0.0031205875, 0.0937197255 66 67 Predictive distribution ~ N(-0.61566, 1.00921) 68 69 Add data point (0.36500, 2.22705): 70 71 Postirior mean: 72 0.9107404583 73 1.9265225090 74 3.1119408740 75 4.1312734131 76 77 Posterior variance:
78 0.0051731092, -0.0004872471, -0.0085815201, 0.0008842340