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.

Ex Input:
We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d. samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for Erdős-Rényi graphs in a certain dense setting.

Ex Output:
On the Information Theoretic Limits of Learning Ising Models


Ex Input:
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it involves solving an N × N eigenvalue system where N is the training set size, making its computational requirements in both memory and time prohibitive for large-scale problems. Various approximation techniques have been developed for KCCA. A commonly used approach is to first transform the original inputs to an M -dimensional random feature space so that inner products in the feature space approximate kernel evaluations, and then apply linear CCA to the transformed inputs. In many applications, however, the dimensionality M of the random feature space may need to be very large in order to obtain a sufficiently good approximation; it then becomes challenging to perform the linear CCA step on the resulting very high-dimensional data matrices. We show how to use a stochastic optimization algorithm, recently proposed for linear CCA and its neuralnetwork extension, to further alleviate the computation requirements of approximate KCCA. This approach allows us to run approximate KCCA on a speech dataset with 1.4 million training samples and a random feature space of dimensionality M = 100000 on a typical workstation.

Ex Output:
LARGE-SCALE APPROXIMATE KERNEL CANONICAL CORRELATION ANALYSIS


Ex Input:
Interlingua based Machine Translation (MT) aims to encode multiple languages into a common linguistic representation and then decode sentences in multiple target languages from this representation. In this work we explore this idea in the context of neural encoder decoder architectures, albeit on a smaller scale and without MT as the end goal. Specifically, we consider the case of three languages or modalities X , Z and Y wherein we are interested in generating sequences in Y starting from information available in X . However, there is no parallel training data available between X and Y but, training data is available between X & Z and Z & Y (as is often the case in many real world applications). Z thus acts as a pivot/bridge. An obvious solution, which is perhaps less elegant but works very well in practice is to train a two stage model which first converts from X to Z and then from Z to Y . Instead we explore an interlingua inspired solution which jointly learns to do the following (i) encodeX and Z to a common representation and (ii) decode Y from this common representation. We evaluate our model on two tasks: (i) bridge transliteration and (ii) bridge captioning. We report promising results in both these applications and believe that this is a right step towards truly interlingua inspired encoder decoder architectures.

Ex Output:

A Correlational Encoder Decoder Architecture for Pivot Based Sequence Generation