Causal discovery from time series data encompasses many existing solutions, including those based on deep learning techniques. However, these methods typically do not endorse one of the most prevalent paradigms in deep learning: End-to-end learning. To address this gap, we explore what we call Causal Pretraining. A methodology that aims to learn a direct mapping from multivariate time series to the underlying causal graphs in a supervised manner. Our empirical findings suggest that causal discovery in a supervised manner is possible, assuming that the training and test time series samples share most of their dynamics. More importantly, we found evidence that the performance of Causal Pretraining can increase with data and model size, even if the additional data do not share the same dynamics. Further, we provide examples where causal discovery for real-world data with causally pretrained neural networks is possible within limits. We argue that this hints at the possibility of a foundation model for causal discovery.

In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradient descent algorithm on a submanifold of the Stiefel manifold to train cPNNs. In case of filters with limited length, we design algorithms for minimizing functionals that approximate the orthogonality constraints imposed on the operators by penalizing the least squares distance to the identity operator. Then, we investigate how scaled cPNNs with a prescribed Lipschitz constant can be used for denoising signals and images, where the achieved quality depends on the Lipschitz constant. Finally, we apply cPNN based denoisers within a Plug-and-Play (PnP) framework and provide convergence results for the corresponding PnP forward-backward splitting algorithm based on an oracle construction.

Visual sentiment analysis is raising more and more attention with the increasing tendency to express emotions through images. While most existing works assign a single dominant emotion to each image, we address the sentiment ambiguity by label distribution learning (LDL), which is motivated by the fact that image usually evokes multiple emotions. Two new algorithms are developed based on conditional probability neural network (CPNN). First, we proposed BCPNN which encodes image label into a binary representation to replace the signless integers used in CPNN, and employ it as a part of input for the neural network. Then, we train our ACPNN model by adding noises to ground truth label and augmenting affective distributions. Since current datasets are mostly annotated for single-label learning, we build two new datasets, one of which is relabeled on the popular Flickr dataset and the other is collected from Twitter. These datasets contain 20,745 images with multiple affective labels, which are over ten times larger than the existing ones. Experimental results show that the proposed methods outperform the state-of-the-art works on our large-scale datasets and other publicly available benchmarks.