Increasingly, copious amounts of consumer data are used to learn high-revenue mechanisms via machine learning. Existing research on mechanism design via machine learning assumes that there is a distribution over the buyers' values for the items for sale and that the learning algorithm's input is a training set sampled from this distribution. This setup makes the strong assumption that no noise is introduced during data collection. In order to help place mechanism design via machine learning on firm foundations, we investigate the extent to which this learning process is robust to noise. Optimizing revenue using noisy data is challenging because revenue functions are extremely volatile: an infinitesimal change in the buyers' values can cause a steep drop in revenue. Nonetheless, we provide guarantees when arbitrarily correlated noise is added to the training set; we only require that the noise has bounded magnitude or is sub-Gaussian. We conclude with an application of our guarantees to multi-task mechanism design, where there are multiple distributions over buyers' values and the goal is to learn a high-revenue mechanism per distribution. To our knowledge, we are the first to study mechanism design via machine learning with noisy data as well as multi-task mechanism design.

Since the attention mechanism is rarely used within the GP literature, we provide a brief review of the topic in this section. Below we follow the description of attention as given by Vaswani et al. [8], including extensions to self-attention and multi-head self-attention. The dot-product attention mechanism [8] takes as input a set of queries, keys and values. The queries and keys have dimension Dz and the values have dimension Dv which may differ from Dz. The operation of dot-product attention then generates weights from the queries and keys which are used to produce a linear mapping of the input values.

Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the challenge of constructing custom kernel functions for high-dimensional GP regression models. Drawing inspiration from recent progress in deep learning, we introduce a novel approach named KITT: Kernel Identification Through Transformers. KITT exploits a transformer-based architecture to generate kernel recommendations in under 0.1 seconds, which is several orders of magnitude faster than conventional kernel search algorithms. We train our model using synthetic data generated from priors over a vocabulary of known kernels. By exploiting the nature of the selfattention mechanism, KITT is able to process datasets with inputs of arbitrary dimension. We demonstrate that kernels chosen by KITT yield strong performance over a diverse collection of regression benchmarks.

Spectral embedding is a powerful graph embedding technique that has received a lot of attention recently due to its effectiveness on Graph Transformers. However, from a theoretical perspective, the universal expressive power of spectral embedding comes at the price of losing two important invariance properties of graphs, sign and basis invariance, which also limits its effectiveness on graph data. To remedy this issue, many previous methods developed costly approaches to learn new invariants and suffer from high computation complexity. In this work, we explore a minimal approach that resolves the ambiguity issues by directly finding canonical directions for the eigenvectors, named Laplacian Canonization (LC). As a pure pre-processing method, LC is light-weighted and can be applied to any existing GNNs. We provide a thorough investigation, from theory to algorithm, on this approach, and discover an efficient algorithm named Maximal Axis Projection (MAP) that works for both sign and basis invariance and successfully canonizes more than 90% of all eigenvectors. Experiments on real-world benchmark datasets like ZINC, MOLTOX21, and MOLPCBA show that MAP consistently outperforms existing methods while bringing minimal computation overhead.

This work presents a data-driven approach for the indoor localization of an observer on a 2D topological map of the environment. State-of-the-art techniques may yield accurate estimates only when they are tailor-made for a specific data modality like camera-based system that prevents their applicability to broader domains. Here, we establish a modality-agnostic framework (called OT-Isomap) and formulate the localization problem in the context of parametric manifold learning while leveraging optimal transportation. This framework allows jointly learning a lowdimensional embedding as well as correspondences with a topological map. We examine the generalizability of the proposed algorithm by applying it to data from diverse modalities such as image sequences and radio frequency signals. The experimental results demonstrate decimeter-level accuracy for localization using different sensory inputs.