In this repo we have applied Conditional Neural Processes to time series prediction. This work is based on the work from Amsterdam Machine Learning lab (https://github.com/AMLab-Amsterdam/FNP)

Based on the work from Amsterdam Machine Learning lab ('The Functional Neural Process'. Christos Louizos, Xiahan Shi, Klamer Schutte, Max Welling, arXiv:1906.08324, 2019. https://arxiv.org/abs/1906.08324)

A neural network (NN) is a parametrized function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a non-parametric probabilistic model that defines a distribution over possible functions, and is updated with new data via the rules of bayesian inference. GPs are probabilistic, data-efficient and flexible, however they are also computationally intensive and thus limited in their applicability.

Neural Processes (NP) are a class of neural latent variable models that:

• defines distributions over functions,
• capable of rapid adaptation to new observations, and
• can estimate the uncertainty in their predictions (just as GP do).

Functional Neural Processes (FNP) don't require explicit global latent variables in their construction as NP, but they rather operate by building a graph of dependencies among local latent variables, reminiscing more of autoencoder type of latent variable models. Neural Processes (NPs) define distributions over global latent variables in terms of subsets of the data, while Attentive Neural Processes (ANP) are extend NPs with a deterministic path that has across-attention mechanism among the datapoints. In a sense, FNPs can be seen as a variant where we discard the global latent variables and instead incorporate cross-attention in the form of a dependency graph among local latent variables.

An Attention Mechanism (AM) enables a neural network to focus only on relevant parts of input data instead of trying to deal with all data when doing a prediction task. AM learns in witch part of the dataset in a similar way than Neural Turing Machines (NTM), it is focusing everywhere, just to different extents. Neural Turing Machines combine a RNN with an external memory store in order to Neural Network write and read from this memory everywhere, just to different extents at each step. Instead of specifying a single location, the RNN outputs an 'attention distribution' that describes how we spread out the amount we care about different memory positions. With the same logic an 'attention distribution' describes how much we write at every location. We do this by having the new value of a position in memory be a convex combination of the old memory content and the write value, with the position between the two decided by the attention weight. To decide which positions in memory to focus their attention on, an NTM use a combination of two different methods:

• Content-based attention. Search through their memory and focus on places that match what they’re looking for.
• Location-based attention. Allows relative movement in memory, enabling the NTM to loop.

Source: https://github.com/Javihaus/Advanced-Time-series-analysis/blob/main/RNN_Pytorch.ipynb

• 'The Functional Neural Process'. Christos Louizos, Xiahan Shi, Klamer Schutte, Max Welling, arXiv:1906.08324, 2019. https://arxiv.org/abs/1906.08324
• 'Cross Attention Network for Few-shot Classification'. Ruibing Hou, Hong Chang, Bingpeng Ma, Shiguang Shan, Xilin Chen , arXiv:1910.07677, 2019 (https://arxiv.org/abs/1910.07677)
• 'Attention and Augmented Recurrent Neural Networks', Olah and Carter, Distill, 2016. (http://distill.pub/2016/augmented-rnns)