Due to the usefulness in data enrichment for data analysis tasks, joinable table discovery has become an important operation in data lake management. Existing approaches target equi-joins, the most common way of combining tables for creating a unified view, or semantic joins, which tolerate misspellings and different formats to deliver more join results. They are either exact solutions whose running time is linear in the sizes of query column and target table repository or approximate solutions lacking precision. In this paper, we propose Deepjoin, a deep learning model for accurate and efficient joinable table discovery. Our solution is an embedding-based retrieval, which employs a pre-trained language model (PLM) and is designed as one framework serving both equi- and semantic joins. We propose a set of contextualization options to transform column contents to a text sequence. The PLM reads the sequence and is fine-tuned to embed columns to vectors such that columns are expected to be joinable if they are close to each other in the vector space. Since the output of the PLM is fixed in length, the subsequent search procedure becomes independent of the column size. With a state-of-the-art approximate nearest neighbor search algorithm, the search time is logarithmic in the repository size. To train the model, we devise the techniques for preparing training data as well as data augmentation. The experiments on real datasets demonstrate that by training on a small subset of a corpus, Deepjoin generalizes to large datasets and its precision consistently outperforms other approximate solutions'. Deepjoin is even more accurate than an exact solution to semantic joins when evaluated with labels from experts. Moreover, when equipped with a GPU, Deepjoin is up to two orders of magnitude faster than existing solutions.

Localisation with Frequency-Modulated Continuous-Wave (FMCW) radar has gained increasing interest due to its inherent resistance to challenging environments. However, complex artefacts of the radar measurement process require appropriate uncertainty estimation to ensure the safe and reliable application of this promising sensor modality. In this work, we propose a multi-session map management system which constructs the best maps for further localisation based on learned variance properties in an embedding space. Using the same variance properties, we also propose a new way to introspectively reject localisation queries that are likely to be incorrect. For this, we apply robust noise-aware metric learning, which both leverages the short-timescale variability of radar data along a driven path (for data augmentation) and predicts the downstream uncertainty in metric-space-based place recognition. We prove the effectiveness of our method over extensive cross-validated tests of the Oxford Radar RobotCar and MulRan dataset. In this, we outperform the current state-of-the-art in radar place recognition and other uncertainty-aware methods when using only single nearest-neighbour queries. We also show consistent performance increases when rejecting queries based on uncertainty over a difficult test environment, which we did not observe for a competing uncertainty-aware place recognition system.

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.

Former President Donald Trump defends himself against allegations he mishandled classified documents on'Special Report.' Former President Donald Trump's trial on 37 federal felony counts is poised to begin on August 14, a judge announced Tuesday. Federal Judge Aileen Cannon announced the preliminary court date Tuesday, but the final date for Trump's trial is likely to change as the former president's legal team is expected to request a delay. Trump has vowed to continue his 2024 presidential campaign despite his legal jeopardy. Trump is accused of 37 counts, including willful retention of national defense information, conspiracy to obstruct justice and making false statements.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about the graph, its subgraphs or nodes themselves. A practical challenge with using embeddings is that there are many available variants to choose from. Selecting a small set of most promising embeddings from the long list of possible options for a given task is challenging and often requires domain expertise. Embeddings can be categorized into two main types: classical embeddings and structural embeddings. Classical embeddings focus on learning both local and global proximity of nodes, while structural embeddings learn information specifically about the local structure of nodes' neighbourhood. For classical node embeddings there exists a framework which helps data scientists to identify (in an unsupervised way) a few embeddings that are worth further investigation. Unfortunately, no such framework exists for structural embeddings. In this paper we propose a framework for unsupervised ranking of structural graph embeddings. The proposed framework, apart from assigning an aggregate quality score for a structural embedding, additionally gives a data scientist insights into properties of this embedding. It produces information which predefined node features the embedding learns, how well it learns them, and which dimensions in the embedded space represent the predefined node features. Using this information the user gets a level of explainability to an otherwise complex black-box embedding algorithm.

Conjectures have historically played an important role in the development of pure mathematics. We propose a systematic approach to finding abstract patterns in mathematical data, in order to generate conjectures about mathematical inequalities, using machine intelligence. We focus on strict inequalities of type f < g and associate them with a vector space. By geometerising this space, which we refer to as a conjecture space, we prove that this space is isomorphic to a Banach manifold. We develop a structural understanding of this conjecture space by studying linear automorphisms of this manifold and show that this space admits several free group actions. Based on these insights, we propose an algorithmic pipeline to generate novel conjectures using geometric gradient descent, where the metric is informed by the invariances of the conjecture space. As proof of concept, we give a toy algorithm to generate novel conjectures about the prime counting function and diameters of Cayley graphs of non-abelian simple groups. We also report private communications with colleagues in which some conjectures were proved, and highlight that some conjectures generated using this procedure are still unproven. Finally, we propose a pipeline of mathematical discovery in this space and highlight the importance of domain expertise in this pipeline.

Unsupervised hashing has received extensive research focus on the past decade, which typically aims at preserving a predefined metric (i.e. Euclidean metric) in the Hamming space. To this end, the encoding functions of the existing hashing are typically quasi-isometric, which devote to reducing the quantization loss from the target metric space to the discrete Hamming space. However, it is indeed problematic to directly minimize such error, since such mentioned two metric spaces are heterogeneous, and the quasi-isometric mapping is non-linear. The former leads to inconsistent feature distributions, while the latter leads to problematic optimization issues. In this paper, we propose a novel unsupervised hashing method, termed Sparsity-Induced Generative Adversarial Hashing (SiGAH), to encode large-scale high-dimensional features into binary codes, which well solves the two problems through a generative adversarial training framework. Instead of minimizing the quantization loss, our key innovation lies in enforcing the learned Hamming space to have similar data distribution to the target metric space via a generative model. In particular, we formulate a ReLU-based neural network as a generator to output binary codes and an MSE-loss based auto-encoder network as a discriminator, upon which a generative adversarial learning is carried out to train hash functions. Furthermore, to generate the synthetic features from the hash codes, a compressed sensing procedure is introduced into the generative model, which enforces the reconstruction boundary of binary codes to be consistent with that of original features. Finally, such generative adversarial framework can be trained via the Adam optimizer. Experimental results on four benchmarks, i.e., Tiny100K, GIST1M, Deep1M, and MNIST, have shown that the proposed SiGAH has superior performance over the state-of-the-art approaches.

As ecommerce continues growing, huge investments in ML and NLP for Information Retrieval are following. While the vector space model dominated retrieval modelling in product search - even as vectorization itself greatly changed with the advent of deep learning -, our position paper argues in a contrarian fashion that program synthesis provides significant advantages for many queries and a significant number of players in the market. We detail the industry significance of the proposed approach, sketch implementation details, and address common objections drawing from our experience building a similar system at Tooso.

The existing supervised relation extraction methods have achieved impressive performance in a closed-set setting, where the relations during both training and testing remain the same. In a more realistic open-set setting, unknown relations may appear in the test set. Due to the lack of supervision signals from unknown relations, a well-performing closed-set relation extractor can still confidently misclassify them into known relations. In this paper, we propose an unknown-aware training method, regularizing the model by dynamically synthesizing negative instances. To facilitate a compact decision boundary, ``difficult'' negative instances are necessary. Inspired by text adversarial attacks, we adaptively apply small but critical perturbations to original training instances and thus synthesizing negative instances that are more likely to be mistaken by the model as known relations. Experimental results show that this method achieves SOTA unknown relation detection without compromising the classification of known relations.