birt-gd 0.1.6

BIRTGD is an implementation of Beta3-irt using gradient descent.

birt-gd

BIRTGD is an implementation of Beta3-irt using gradient descent.

The model expects to receive two sets of data, X being a list or array containing tuples of indices, where the first index references the instance j and the second index of the tuple references the model i, thus, Y will be a list or array where each input will be p_ij ~ Β(α_ij, β_ij), the probability of the i model correctly classifying the j model. Being,

p_ij ~ Β(α_ij, β_ij)

α_ij = F_α(θ_i, δ_j, a_j) = (θ_i/δ_j)^a_j

β_ij = F_β(θ_i, δ_j, a_j) = ( (1 - θ_i)/(1 - δ_j) )^a_j

θ_i ~ Β(1,1), δ_j ~ Β(1,1), a_j ~ N(1, σ²₀)

where,

E[p_ij | θ_i, δ_j, a_j] = (α_ij)/( α_ij + β_ij) = 1/(1 + ( (δ_j)/(1 - δ_j) )^a_j × ( (θ_i)/(1 - θ_i) ) ^{- a_j} )

Installation

Dependencies

birt-sgd requires:

• Python (>=3.8.5)
• numpy (>=1.19.5)
• tqdm (>=4.59.0)
• tensorflow (>=2.4.1)
• pandas (>=1.2.3)

User installation

pip install -i https://test.pypi.org/simple/ birt-gd

Source code

You can check the code with

git clone https://github.com/Manuelfjr/birt-gd

Usage

Import the BIRTGD's class

>>> from birt import BIRTGD

>>> X = [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]
>>> Y = [0.98,0.81,0.12,0.567,0.76,0.9]

>>> bgd = BIRTGD(n_models=3, n_instances=2, random_seed=1)
>>> bgd.fit(X,Y)
100%|██████████| 20/20 [00:00<00:00, 52.81it/s]
<birt.BIRTGD at 0x7f6ce2555f50>

>>> bgd.abilities
array([0.78665066, 0.5025896 , 0.545207], dtype=float32)

>>> bgd.difficulties
array([0.25070453, 0.46883535], dtype=float32)

>>> bgd.discriminations
array([0.09374281, 1.4122988 ], dtype=float32)

Summary data

How to use the summary feature:

• Generate data

import numpy as np

m, n = 5, 20
np.random.seed(1)
abilities = [np.random.beta(1,i) for i in ([0.1, 10] + [1]*(m-2))]
difficulties = [np.random.beta(1,i) for i in [10, 5] + [1]*(n-2)]
discrimination = list(np.random.normal(1,1, size=n))
pij = pd.DataFrame(columns=range(m), index=range(n))

• Fitting the model

birt = BIRTGD(n_models=pij.shape[1],
             n_instances=pij.shape[0],
             learning_rate=1,
             epochs=5000,
             n_inits=1000)
birt.fit(pij)

• Summary

birt.summary()

        HYPERPARAMS
        -----
                        | Min      1Qt      Median   3Qt      Max      Std.Dev
        Ability         | 0.00010  0.22148  0.63389  0.73353  0.92040  0.33960
        Difficulty      | 0.01745  0.28047  0.63058  0.84190  0.98624  0.31635
        Discrimination  | 0.31464  1.28330  1.61493  2.22936  4.44645  1.02678
        pij             | 0.00000  0.02219  0.35941  0.86255  0.99993  0.40210
        -----
        Pseudo-R2       | 0.90381
        

Using Plot Feature

birt.plot(xaxis='discrimination',yaxis='difficulty', ann=True, kwargs={'color': 'red'})

birt.plot(xaxis='difficulty',yaxis='average_item', ann=True, kwargs={'color': 'red'})

birt.plot(xaxis='ability',yaxis='average_response', ann=False)

Help and Support

Communication

• E-mail: [e-mail]
• Site: https://manuelfjr.github.io/

License

MIT License

Copyright (c) 2021 Manuel

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.