jiangnanhugo

1. General Background and Overview

• Probabilistic Data Structures for Web Analytics and Data Mining : A great overview of the space of probabilistic data structures and how they are used in approximation algorithm implementation.
• Models and Issues in Data Stream Systems
• Philippe Flajolet’s contribution to streaming algorithms : A presentation by Jérémie Lumbroso that visits some of the hostorical perspectives and how it all began with Flajolet
• Approximate Frequency Counts over Data Streams by Gurmeet Singh Manku & Rajeev Motwani : One of the early papers on the subject.
• [Methods for Finding Frequent Items in Data Streams](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.9800&rep

jiangnanhugo

jiangnanhugo

import theano as T
def nce_binary_conditional_likelihood(p_unnormalized,y,y_flat,noise_samples,noise_dist,k):
    p_unnormalized_exp=T.exp(p_unnormalized)
    p_unnormalized_flat=p_unnormalized_exp.flatten()
    unnorm_y=p_unnormalized_flat[y_flat]
    noise_y=noise_dist[y]
    pos_cost=T.log(unnorm_y/(unnorm_y+k*noise_y))
    
    neg_cost=T.log(k*noise_dist/(p_unnormalized_exp+k*noise_dist))
    return -T.mean(pos_cost+ T.sum(neg_cost*noise_samples,axis=1),dtype=theano.config.floatX)

jiangnanhugo

from collections import OrderedDict
import numpy as np
import theano
import theano.tensor as T
from theano.ifelse import ifelse


def cg(loss, params, x0=None, max_iters=100, precondition=None, tol=1e-3,
       conv_crit='cg'):
    """(Preconditioned) Conjugate Gradient (CG) updates

jiangnanhugo

# See for details and discussion: https://github.com/Theano/Theano/issues/4087
import theano
from theano import tensor as T, ifelse
from theano.gof import Variable


def fast_jacobian(expr, wrt, chunk_size=16, func=None):
    assert isinstance(expr, Variable), \
        "tensor.jacobian expects a Variable as `expr`"
    assert expr.ndim < 2, \