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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!