Implementing Adagrad in Python

Question

I'm trying to implement Adagrad in Python. For learning purposes, I am using matrix factorisation as an example. I'd be using Autograd for computing the gradients.

My main question is if the implementation is fine.

Problem description

Given a matrix A (M x N) having some missing entries, decompose into W and H having sizes (M x k) and (k X N) respectively. Goal would to learn W and H using Adagrad. I'd be following this guide for the Autograd implementation.

NB: I very well know that ALS based implementation are well-suited. I'm using Adagrad only for learning purposes

Customary imports

import autograd.numpy as np
import pandas as pd

Creating the matrix to be decomposed

A = np.array([[3, 4, 5, 2],
                   [4, 4, 3, 3],
                   [5, 5, 4, 3]], dtype=np.float32).T

Masking one entry

A[0, 0] = np.NAN

Defining the cost function

def cost(W, H):
    pred = np.dot(W, H)
    mask = ~np.isnan(A)
    return np.sqrt(((pred - A)[mask].flatten() ** 2).mean(axis=None))

Decomposition params

rank = 2
learning_rate=0.01
n_steps = 10000

Gradient of cost wrt params W and H

from autograd import grad, multigrad
grad_cost= multigrad(cost, argnums=[0,1])

Main Adagrad routine (this needs to be checked)

shape = A.shape

# Initialising W and H
H =  np.abs(np.random.randn(rank, shape[1]))
W =  np.abs(np.random.randn(shape[0], rank))

# gt_w and gt_h contain accumulation of sum of gradients
gt_w = np.zeros_like(W)
gt_h = np.zeros_like(H)

# stability factor
eps = 1e-8
print "Iteration, Cost"
for i in range(n_steps):

    if i%1000==0:
        print "*"*20
        print i,",", cost(W, H)

    # computing grad. wrt W and H
    del_W, del_H = grad_cost(W, H)

    # Adding square of gradient
    gt_w+= np.square(del_W)
    gt_h+= np.square(del_H)

    # modified learning rate
    mod_learning_rate_W = np.divide(learning_rate, np.sqrt(gt_w+eps))
    mod_learning_rate_H = np.divide(learning_rate, np.sqrt(gt_h+eps))
    W =  W-del_W*mod_learning_rate_W
    H =  H-del_H*mod_learning_rate_H

While the problem converges and I get a reasonable solution, I was wondering if the implementation is correct. Specifically, if the understanding of sum of gradients and then computing the adaptive learning rate is correct or not?

Answer 1

At a cursory glance, your code closely matches that at https://github.com/benbo/adagrad/blob/master/adagrad.py

del_W, del_H = grad_cost(W, H)

matches

grad=f_grad(w,sd,*args)

gt_w+= np.square(del_W)
gt_h+= np.square(del_H)

matches

gti+=grad**2

mod_learning_rate_W = np.divide(learning_rate, np.sqrt(gt_w+eps))
mod_learning_rate_H = np.divide(learning_rate, np.sqrt(gt_h+eps))

matches

adjusted_grad = grad / (fudge_factor + np.sqrt(gti))

W =  W-del_W*mod_learning_rate_W
H =  H-del_H*mod_learning_rate_H

matches

w = w - stepsize*adjusted_grad

So, assuming that adagrad.py is correct and the translation is correct, would make your code correct. (consensus does not prove your code to be right, but it could be a hint)