Download A Collaborative Kalman Filter for Time

A Collaborative Kalman Filter
for Time-Evolving
Dyadic Processes
Reporter: Wei Lin
S. Gultekin and J. Paisley. A collaborative Kalman filter for time-evolving dyadic
processes, IEEE International Conference on Data Mining (ICDM), Shenzhen, China,
2014
Outline
1. An introduction of the related problem
2. The related approaches and model
> Collaborative filtering with matrix factorization
> Kalman filter
> Collaborative Kalman Filter
3. Experiment
> stock data
4. Further work
Problem
the only aim of the research in finance market is predicting the
trendency ,But what the information that we can use?
only use its own history to predict its future?
3
this text show that the behavior of all stocks in SH contain large
amounts of information about the market ,so we need to consider the
trading information of thousands of stocks jointly every day.
volume
the relativity in
time and space
price
The trading data from 1000 stocks in Shanghai
How do we deal with Such a high dimensional problem ,note that the
samples are not so big ! ! ( nearly 20 years * nearly 200 trading
days=4000) .
Using Deep Learning dirctly will work ??
The related approaches and model
Collaborative filtering with matrix factorization
ui represent the locations of each user in a
latent space and wj represent the locations
of each object in the same latent space.
their locations in the latent space imply the
similarity in user's taste. But this relativity is
fixed , not change with time go by.
matrix factorization model
6
Kalman filter
first-order Markov process
prior
posterior
update
Collaborative Kalman Filter
At any given time t, the output for dyad (i, j)
uses the dot product <ui[t], wj[t]>
Prior model
The CKF models each latent location of a user or object as moving in space
according to a Brownian motion
Hyperprior model
We develop the CKF model by allowing α to dynamically change in time as well.
variational approximation
variational objective function
Coordinate update of q(u)
q(w) is similar to q(u)
Inferring the geometric Brownian motion exp{a[t]}
We derive a point estimate for a[t] ,we approximate the relevant terms in
L using a second order Taylor expansion about the point a[t−Δt]
be the eigendecomposition of the posterior covariance
of ui at the previous observation
Let
Then we have
Experiment
Stock returns data measured at opening and closing times for 433 companies
from the AMEX exchange,2,774 companies from NASDAQ and 3,273 companies
from the NYSE for a total of 6,480 stocks and 39.1million total measurements
from 1962–2014
ps : There is only one state vector corresponding to w, which we
refer to as a “state-of-the-world”
The drift parameter a(t) can be used to analyse the volatility of each stock
Further work
1. We can extend the first-order Markov process, which make the
prediction of the position of the latent variable in the next moment
have the have the direction, not just a Brownian motion
2. We can introduce other machine learning algorithm to the
latent variable space, in order to dig up the law of the motion in
the latent variable space. ps. this is no longer a high
dimensional problem, but it contains much information about all
stocks and the marketing environment.
Thank You!