Part 1. Definition
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Part 2. Example
We propose a local coherence model based on a convolutional neural network that operates over the entity grid representation of a text. The model captures long range entity transitions along with entity-specific features without loosing generalization, thanks to the power of distributed representation. We present a pairwise ranking method to train the model in an end-to-end fashion on a task and learn task-specific high level features. Our evaluation on three different coherence assessment tasks demonstrates that our model achieves state of the art results outperforming existing models by a good margin.
Answer: A Neural Local Coherence Model
Explanation: This statement "A Neural Local Coherence Model" is taken from the subtext "convolutional neural network" and its explanation in the passage. This is a positive example because the title belongs to the mentions in the passage
Part 3. Exercise
We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with M 3 components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro [21]. Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least 1 e. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.
Answer:
Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences