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:
Here, we propose a brain-inspired winner-take-all emotional neural network (WTAENN) and prove the universal approximation property for the novel architecture. WTAENN is a single layered feedforward neural network that benefits from the excitatory, inhibitory, and expandatory neural connections as well as the winner-take-all (WTA) competitions in the human brain’s nervous system. The WTA competition increases the information capacity of the model without adding hidden neurons. The universal approximation capability of the proposed architecture is illustrated on two example functions, trained by a genetic algorithm, and then applied to several competing recent and benchmark problems such as in curve fitting, pattern recognition, classification and prediction. In particular, it is tested on twelve UCI classification datasets, a facial recognition problem, three real world prediction problems (2 chaotic time series of geomagnetic activity indices and wind farm power generation data), two synthetic case studies with constant and nonconstant noise variance as well as k-selector and linear programming problems. Results indicate the general applicability and often superiority of the approach in terms of higher accuracy and lower model complexity, especially where low computational complexity is

Ex Output:
A Winner-Take-All Approach to Emotional Neural Networks with Universal Approximation Property


Ex Input:
Techniques for plan recogmtwn under uncer­ tainty require a stochastic model of the plan­ generation process. We introduce probabilistic state-dependent grammars (PSDGs) to represent an agent's plan-generation process. The PSDG language model extends probabilistic context­ free grammars (PCFGs) by allowing production probabilities to depend on an explicit model of the planning agent's internal and external state. Given a PSDG description of the plan-generation process, we can then use inference algorithms that exploit the particular independence proper­ ties of the PSDG language to efficiently answer plan-recognition queries. The combination of the PSDG language model and inference algorithms extends the range of plan-recognition domains for which practical probabilistic inference is pos­ sible, as illustrated by applications in traffic mon­ itoring and air combat.

Ex Output:

Probabilistic State-Dependent Grammars for Plan Recognition