However, categorical features present a unique challenge as they require embedding a typically vast vocabulary into a smaller vector space for further calculations.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems.

High-cardinality categorical features are a major challenge for machine learning methods in general and for deep learning in particular. Existing solutions such as one-hot encoding and entity embeddings can be hard to scale when the cardinality is very high, require much space, are hard to interpret or may overfit the data. A special scenario of interest is that of repeated measures, where the categorical feature is the identity of the individual or object, and each object is measured several times, possibly under different conditions (values of the other features). We propose accounting for high-cardinality categorical features as random effects variables in a regression setting, and consequently adopt the corresponding negative log likelihood loss from the linear mixed models (LMM) statistical literature and integrate it in a deep learning framework. We test our model which we call LMMNN on simulated as well as real datasets with a single categorical feature with high cardinality, using various baseline neural networks architectures such as convolutional networks and LSTM, and various applications in e-commerce, healthcare and computer vision. Our results show that treating high-cardinality categorical features as random effects leads to a significant improvement in prediction performance compared to state of the art alternatives. Potential extensions such as accounting for multiple categorical features and classification settings are discussed. Our code and simulations are available at https://github.com/gsimchoni/lmmnn.

This paradigm challenges traditional data management and analysis techniques by demanding innovative solutions capable of processing, analyzing, and deriving insights from vast and diverse datasets. In particular, the inclusion of mixed data types, such as numerical and categorical variables, poses significant challenges to conventional methodologies, necessitating the development of novel approaches to effectively leverage the wealth of information available [2]. Traditionally, data handling methods were designed around homogeneous datasets, typically consisting of numerical values. However, the big data paradigm introduces a multitude of data types, including structured, unstructured, and semi-structured data, which demand a departure from traditional approaches. Moreover, the three primary characteristics of big data--volume, velocity, and variety--amplify the complexity of data analysis, requiring scalable and adaptable solutions capable of processing large volumes of data at high speeds while accommodating diverse data formats and structures. These methods for handling mixed data often involve separate analyses of categorical and numerical variables, treating them as distinct entities rather than integrating their interdependencies.

This article presents a novel pretopology-based algorithm designed to address the challenges of clustering mixed data without the need for dimensionality reduction. Leveraging Disjunctive Normal Form, our approach formulates customizable logical rules and adjustable hyperparameters that allow for user-defined hierarchical cluster construction and facilitate tailored solutions for heterogeneous datasets. Through hierarchical dendrogram analysis and comparative clustering metrics, our method demonstrates superior performance by accurately and interpretably delineating clusters directly from raw data, thus preserving data integrity. Empirical findings highlight the algorithm's robustness in constructing meaningful clusters and reveal its potential in overcoming issues related to clustered data explainability. The novelty of this work lies in its departure from traditional dimensionality reduction techniques and its innovative use of logical rules that enhance both cluster formation and clarity, thereby contributing a significant advancement to the discourse on clustering mixed data.

We study streaming data with categorical features where the vocabulary of categorical feature values is changing and can even grow unboundedly over time. Feature hashing is commonly used as a pre-processing step to map these categorical values into a feature space of fixed size before learning their embeddings. While these methods have been developed and evaluated for offline or batch settings, in this paper we consider online settings. We show that deterministic embeddings are sensitive to the arrival order of categories and suffer from forgetting in online learning, leading to performance deterioration. To mitigate this issue, we propose a probabilistic hash embedding (PHE) model that treats hash embeddings as stochastic and applies Bayesian online learning to learn incrementally from data. Based on the structure of PHE, we derive a scalable inference algorithm to learn model parameters and infer/update the posteriors of hash embeddings and other latent variables. Our algorithm (i) can handle an evolving vocabulary of categorical items, (ii) is adaptive to new items without forgetting old items, (iii) is implementable with a bounded set of parameters that does not grow with the number of distinct observed values on the stream, and (iv) is invariant to the item arrival order. Experiments in classification, sequence modeling, and recommendation systems in online learning setups demonstrate the superior performance of PHE while maintaining high memory efficiency (consumes as low as 2~4 memory of a one-hot embedding table). Supplementary materials are at https://github.com/aodongli/probabilistic-hash-embeddings

Handling missing data remains a fundamental challenge in real-world tabular datasets, especially when data are heterogeneous with both numerical and categorical features. Existing imputation methods often fail to capture complex structural dependencies and handle heterogeneous data effectively. We present \textbf{IVGAE}, a Variational Graph Autoencoder framework for robust imputation of incomplete heterogeneous data. IVGAE constructs a bipartite graph to represent sample-feature relationships and applies graph representation learning to model structural dependencies. A key innovation is its \textit{dual-decoder architecture}, where one decoder reconstructs feature embeddings and the other models missingness patterns, providing structural priors aware of missing mechanisms. To better encode categorical variables, we introduce a Transformer-based heterogeneous embedding module that avoids high-dimensional one-hot encoding. Extensive experiments on 16 real-world datasets show that IVGAE achieves consistent improvements in RMSE and downstream F1 across MCAR, MAR, and MNAR missing scenarios under 30\% missing rates. Code and data are available at: https://github.com/echoid/IVGAE.

Fair clustering has gained increasing attention in recent years, especially in applications involving socially sensitive attributes. However, existing fair clustering methods often lack inter-pretability, limiting their applicability in high-stakes scenarios where understanding the rationale behind clustering decisions is essential. In this work, we address this limitation by proposing an interpretable and fair clustering framework, which integrates fairness constraints into the structure of decision trees. Our approach constructs interpretable decision trees that partition the data while ensuring fair treatment across protected groups. To further enhance the practicality of our framework, we also introduce a variant that requires no fairness hyperparameter tuning, achieved through post-pruning a tree constructed without fairness constraints. Extensive experiments on both real-world and synthetic datasets demonstrate that our method not only delivers competitive clustering performance and improved fairness, but also offers additional advantages such as interpretability and the ability to handle multiple sensitive attributes. These strengths enable our method to perform robustly under complex fairness constraints, opening new possibilities for equitable and transparent clustering.

Adversarial attacks on tabular data present unique challenges due to the heterogeneous nature of mixed categorical and numerical features. Unlike images where pixel perturbations maintain visual similarity, tabular data lacks intuitive similarity metrics, making it difficult to define imperceptible modifications. Additionally, traditional gradient-based methods prioritise $\ell_p$-norm constraints, often producing adversarial examples that deviate from the original data distributions. To address this, we propose a latent-space perturbation framework using a mixed-input Variational Autoencoder (VAE) to generate statistically consistent adversarial examples. The proposed VAE integrates categorical embeddings and numerical features into a unified latent manifold, enabling perturbations that preserve statistical consistency. We introduce In-Distribution Success Rate (IDSR) to jointly evaluate attack effectiveness and distributional alignment. Evaluation across six publicly available datasets and three model architectures demonstrates that our method achieves substantially lower outlier rates and more consistent performance compared to traditional input-space attacks and other VAE-based methods adapted from image domain approaches, achieving substantially lower outlier rates and higher IDSR across six datasets and three model architectures. Our comprehensive analyses of hyperparameter sensitivity, sparsity control, and generative architecture demonstrate that the effectiveness of VAE-based attacks depends strongly on reconstruction quality and the availability of sufficient training data. When these conditions are met, the proposed framework achieves superior practical utility and stability compared with input-space methods. This work underscores the importance of maintaining on-manifold perturbations for generating realistic and robust adversarial examples in tabular domains.

This paper presents the key algorithmic techniques behind CatBoost, a new gradient boosting toolkit.