LICD has 577 features and labels. The dataset provides several ML research opportunities; we discuss two demonstration experiments.

M-step mainly consists of the weighted sum of partial derivative. Thus the complexity of regular E-step takes O(Nkd), and O(Nk(L+d)) for OT-based E step where L is the number of iterations of Sinkhorn's algorithm. The complexity of M-step takes O(Nkd).

Variational autoencoders (VAEs) are one of the powerful likelihood-based generative models with applications in many domains.

We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key statistics such as conditional quantiles, mean, and covariance. It offers streamlined learning via a single unconditional training phase, allowing efficient inference without the need for retraining even when conditioning changes. By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of complex probability distributions. We provide theoretical guarantees that ensure both optimization consistency and statistical accuracy. In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods. This demonstrates that a a minimalistic architecture with a theoretically grounded loss can achieve competitive results, even in the face of more complex architectures.

Our approach is fully unsupervised and can lead to high quality correspondences even in challenging cases such as sparse point clouds or non-isometric meshes, where current methods fail. Our first key observation is that, in line with neural priors observed in other domains, recent network architectures on 3D data, even without training, tend to produce pointwise features that induce plausible maps between rigid or non-rigid shapes. Secondly, we show that given a noisy map as input, training a feature extraction network with the input map as supervision, tends to remove artifacts from the input and can act as a powerful correspondence denoising mechanism, both between individual pairs and within a collection. With these observations in hand, we propose a two-stage unsupervised paradigm for shape matching, by (i) performing unsupervised training by adapting an existing approach to obtain an initial set of noisy matches, (ii) using these matches to train a network in a supervised manner. We demonstrate that this approach significantly improves the accuracy of the maps, especially when trained within a collection. We show that NCP is data-efficient, fast, and achieves state-of-the-art results on many tasks. Our code will be released after publication.

We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks.

We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key statistics such as conditional quantiles, mean, and covariance. It offers streamlined learning via a single unconditional training phase, allowing efficient inference without the need for retraining even when conditioning changes. By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of complex probability distributions. We provide theoretical guarantees that ensure both optimization consistency and statistical accuracy. In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods.

Our approach is fully unsupervised and can lead to high quality correspondences even in challenging cases such as sparse point clouds or non-isometric meshes, where current methods fail. Our first key observation is that, in line with neural priors observed in other domains, recent network architectures on 3D data, even without training, tend to produce pointwise features that induce plausible maps between rigid or non-rigid shapes. Secondly, we show that given a noisy map as input, training a feature extraction network with the input map as supervision, tends to remove artifacts from the input and can act as a powerful correspondence denoising mechanism, both between individual pairs and within a collection. With these observations in hand, we propose a two-stage unsupervised paradigm for shape matching, by (i) performing unsupervised training by adapting an existing approach to obtain an initial set of noisy matches, (ii) using these matches to train a network in a supervised manner. We demonstrate that this approach significantly improves the accuracy of the maps, especially when trained within a collection.