Prediction generation Predicts how much a user a likes an item i Generate predictions using weighted deviation from the mean B=ra+∑(rn-rn),12a "c: sum of all weights d=∑
11 Prediction Generation ◼ Predicts how much a user a likes an item i ◼ Generate predictions using weighted deviation from the mean ◼ : sum of all weights = + − a u u u i a Pa,i r r , r w , ( ) 1 = Ya u wa u , , (1)
Error estimation Mean absolute Error( MAe for user a ∑|P-zl MAE a Standard deviation of the errors K ∑(ME-MB 1a=1 K 12
12 Error Estimation ◼ Mean Absolute Error (MAE) for user a ◼ Standard Deviation of the errors N P r MAE a i N i a i a | | , 1 , − = = K MAE MAE K a a 2 1 ( − ) = =
EXample 无法显示该图 Correlation a. Sam Dylan Mathey Sammy -0.87 Dylan 0.21 Mathew 0.87 0.21 1 my+Dylan, MatrirrDylan )Sammy, Dyan t Sammy. Mathew =33+{(3-34)1+(2-32)(-0.87)/(1+0.87) Prediction Actual MAE Matrix Titanic Matrix Titanic ME=083 8 Sammy3628340.9 Basil 4.64.1 5075 13
13 Example Sammy Dylan Mathew Sammy 1 1 -0.87 Dylan 1 1 0.21 Users Mathew -0.87 0.21 1 Correlation MAE Matrix Titanic Matrix Titanic Sammy 3.6 2.8 3 4 0.9 Basil 4.6 4.1 4 5 0.75 Prediction Actual Users | | | | 1 ( ) ( ) , , , , , , , Mathew Matrix Mathew Sammy Mathew Sammy Dylan Sammy Mathew Dylan Matrix Dylan Sammy Dylan Matrix Sammy Sammy r r w w w r r w P r + − − + = + 3.6 3.3 {(3 3.4) 1 (2 3.2) ( 0.87)/(1 0.87) = = + − + − − + =0.83 wa,i MAE
Statistical Collaborative Filters Ringo i shardanand and maes 95(MID) Recommends music albums Each user buys certain music artists CDs ∑ Base case: weighted average Pa. Predictions K Mean square difference First compute dissimilarity between pairs of users Then find all users y with dissimilarity less than L Compute the weighted average of ratings of these users Pearson correlation(equation 1) Constrained Pearson correlation (Equation 1 with weighted average of similar users(corr >L)) 14
14 Statistical Collaborative Filters ◼ Ringo [Shardanand and Maes 95 (MIT)] ◼ Recommends music albums ◼ Each user buys certain music artists’ CDs ◼ Base case: weighted average ◼ Predictions ◼ Mean square difference ◼ First compute dissimilarity between pairs of users ◼ Then find all users Y with dissimilarity less than L ◼ Compute the weighted average of ratings of these users ◼ Pearson correlation (Equation 1) ◼ Constrained Pearson correlation (Equation 1 with weighted average of similar users (corr > L)) K P Pa i j a j = ,
Open problems in CF Sparsity problem Crs have poor accuracy and coverage in comparison to population averages at low rating density [gsK+99] First rater problem a The first person to rate an item receives no benefit. CF depends upon altruism. [AZ97 15
15 Open Problems in CF ◼ “Sparsity Problem” ◼ CFs have poor accuracy and coverage in comparison to population averages at low rating density [GSK+99]. ◼ “First Rater Problem” ◼ The first person to rate an item receives no benefit. CF depends upon altruism. [AZ97]