The problem of selecting the best k-element subset from a universe is involved in many applications. While previous studies assumed a noise-free environment or a noisy monotone submodular objective function, this paper considers a more realistic and general situation where the evaluation of a subset is a noisy monotone function (not necessarily submodular), with both multiplicative and additive noises. To understand the impact of the noise, we firstly show the approximation ratio of the greedy algorithm and POSS, two powerful algorithms for noise-free subset selection, in the noisy environments. We then propose to incorporate a noise-aware strategy into POSS, resulting in the new PONSS algorithm. We prove that PONSS can achieve a better approximation ratio under some assumption such as i.i.d.

Multi-layered distributed representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are still the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical distributed representations by stacking several layers of regression GBDTs as its building block. The model can be jointly trained by a variant of target propagation across layers, without the need to derive backpropagation nor differentiability. Experiments confirmed the effectiveness of the model in terms of performance and representation learning ability.

Neural Information Processing Systems http://nips.cc/

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes. In the area of artificial intelligence (AI), the two abilities are usually realised by machine learning and logic programming, respectively. However, the two categories of techniques were developed separately throughout most of the history of AI. In this paper, we present the abductive learning targeted at unifying the two AI paradigms in a mutually beneficial way, where the machine learning model learns to perceive primitive logic facts from data, while logical reasoning can exploit symbolic domain knowledge and correct the wrongly perceived facts for improving the machine learning models. Furthermore, we propose a novel approach to optimise the machine learning model and the logical reasoning model jointly. We demonstrate that by using abductive learning, machines can learn to recognise numbers and resolve unknown mathematical operations simultaneously from images of simple hand-written equations. Moreover, the learned models can be generalised to longer equations and adapted to different tasks, which is beyond the capability of state-ofthe-art deep learning models.

Neural Information Processing Systems http://nips.cc/