TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: We introduce a new and rigorously-formulated PAC-Bayes few-shot meta-learning algorithm that implicitly learns a model prior distribution of interest. Our proposed method extends the PAC-Bayes framework from a single task setting to the few-shot meta-learning setting to upper-bound generalisation errors on unseen tasks. We  also propose a generative-based approach to model the shared prior and task-specific posterior more expressively compared to the usual diagonal Gaussian assumption. We show that the models trained with our proposed meta-learning algorithm are well calibrated and accurate, with state-of-the-art calibration and classification results on mini-ImageNet benchmark, and competitive results in a multi-modal task-distribution regression.

SOLUTION: Bayesian meta-learning using PAC-Bayes framework and implicit prior distributions

PROBLEM: Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are 
 variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods may have large bias. 
 In this work, we aim to improve upon MCMC and VI by a novel hybrid method based on the idea of reducing simulation bias of finite-length MCMC chains using gradient-based optimisation. The proposed method can generate low-biased samples by increasing the length of MCMC simulation and optimising the MCMC hyper-parameters, which offers attractive balance between approximation bias and computational efficiency. We show that our method produces promising results on popular benchmarks when compared to recent hybrid methods of MCMC and VI.

SOLUTION: In this work, we aim to improve upon MCMC and VI by a novel hybrid method based on the idea of reducing simulation bias of finite-length MCMC chains using gradient-based optimisation.

PROBLEM: This is an empirical paper which constructs color invariant networks and evaluates their performances on a realistic data set. The paper studies the simplest possible case of color invariance: invariance under pixel-wise permutation of the color channels. Thus the network is aware not of the specific color object, but its colorfulness. The data set introduced in the paper consists of images showing crashed cars from which ten classes were extracted. An additional annotation was done which labeled whether the car shown was red or non-red.   The networks were evaluated by their performance on the classification task. With the color annotation we altered the color ratios  in the training data and analyzed the generalization capabilities of the networks on the unaltered test data. We further split the test data in red and non-red cars and did a similar evaluation. It is shown in the paper that an pixel-wise ordering of the rgb-values of the images performs better or at least similarly for small deviations from the true color ratios. The limits of these networks are also discussed.

SOLUTION:
We construct and evaluate color invariant neural nets on a novel realistic data set