Learning without Labels and Nonnegative Tensor Factorization

Special thanks to my parents and friends for their love and support. 1 3-way PARAFAC model: The tensor is represented as a linear combination of r rank-1 tensors. This will provide a rank-r approximation to the original A plot of the loglikelihood functions (θ) in the case of classification for k = 1 (left, θ true = 0.75) and k = 2 (right, θ true = (0.8, 0.6) 3 A plot of the loglikelihood function (θ) in the case of regression for k = 1 with θ true = 0.3, τ = 1, µ y = 0 and σ y = 0. 4 Average value of | ˆ θ mle n − θ true | as a function of θ true and p(y = 1) for k = 1 5 Scatter plot contrasting the true and predicted values of θ in the case of a single classifier k = 1, p(y = 1) = 0.8, and n = 500 unlabeled examples.. 36 6 Scatter plot contrasting the true and predicted values of θ in the case of a single regression model k = 1, σ y = 1, and n = 1000 unlabeled examples.. 36 7 Comparison of collaborative and non-collaborative estimation for k = 10 viii 11 mae(ˆ θ mle , θ true) as a function of n for different number of annotators k on RTE (left) and TEMP (right) 12 mae(θ true , ˆ θ mle) as a function of the test set size on the Ringnorm dataset.. . 43 13 mae(ˆ θ mle , θ true) for the domain adaptation (n = 1000, p(y = 1) = 0.75) and 20 newsgroup (n = 15, 000, p(y = 1) = 0.05 for each one-vs-all data). 44 14 Normality of f θ (X)|Y = 1 for different data sets and using different clas