The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this note, we consider the identifiability of state-based causal effects: how an intervention on a particular state of treatment variables affects a particular state of outcome variables. We demonstrate that state-based causal effects may be identifiable even when variable-based causal effects may not. Moreover, we show that this separation occurs only when additional knowledge -- such as context-specific independencies and conditional functional dependencies -- is available. We further examine knowledge that constrains the states of variables, and show that such knowledge does not improve identifiability on its own but can improve both variable-based and state-based identifiability when combined with other knowledge such as context-specific independencies. Our findings highlight situations where causal effects of interest may be estimable from observational data and this identifiability may be missed by existing variable-based frameworks.

People without a database background usually rely on file systems or tools such as Excel for data management, which often lead to redundancy and data inconsistency. Relational databases possess strong data management capabilities, but require a high level of professional expertise from users. Although there are already many works on Text2SQL to automate the translation of natural language into SQL queries for data manipulation, all of them presuppose that the database schema is pre-designed. In practice, schema design itself demands domain expertise, and research on directly generating schemas from textual requirements remains unexplored. In this paper, we systematically define a new problem, called Text2Schema, to convert a natural language text requirement into a relational database schema. With an effective Text2Schema technique, users can effortlessly create database table structures using natural language, and subsequently leverage existing Text2SQL techniques to perform data manipulations, which significantly narrows the gap between non-technical personnel and highly efficient, versatile relational database systems. We propose SchemaAgent, an LLM-based multi-agent framework for Text2Schema. We emulate the workflow of manual schema design by assigning specialized roles to agents and enabling effective collaboration to refine their respective subtasks. We also incorporate dedicated roles for reflection and inspection, along with an innovative error detection and correction mechanism to identify and rectify issues across various phases. Moreover, we build and open source a benchmark containing 381 pairs of requirement description and schema. Experimental results demonstrate the superiority of our approach over comparative work.

Causal Discovery plays a pivotal role in revealing relationships among observed variables, particularly in the temporal setup. While the majority of CD methods rely on synthetic data for evaluation, and recently for training, these fall short in accurately mirroring real-world scenarios; an effect even more evident in temporal data. Generation techniques depending on simplified assumptions on causal structure, effects and time, limit the quality and diversity of the simulated data. In this work, we introduce Temporal Causal-based Simulation (TCS), a robust framework for generating realistic time-series data and their associated temporal causal graphs. The approach is structured in three phases: estimating the true lagged causal structure of the data, approximating the functional dependencies between variables and learning the noise distribution of the corresponding causal model, each part of which can be explicitly tailored based on data assumptions and characteristics. Through an extensive evaluation process, we highlight that single detection methods for generated data discrimination prove inadequate, accentuating it as a multifaceted challenge. For this, we detail a Min-max optimization phase that draws on AutoML techniques. Our contributions include a flexible, model-agnostic pipeline for generating realistic temporal causal data, a thorough evaluation setup which enhances the validity of the generated datasets and insights into the challenges posed by realistic data generation. Through experiments involving not only real but also semi-synthetic and purely synthetic datasets, we demonstrate that while sampling realistic causal data remains a complex task, our method enriches the domain of generating sensible causal-based temporal data.

We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by the causal graph, reducing the set of models considered by the identifiability problem. We formalize the notion of constrained identifiability, which takes a set of constraints as another input to the classical definition of identifiability. We then introduce a framework for testing constrained identifiability by employing tractable Arithmetic Circuits (ACs), which enables us to accommodate constraints systematically. We show that this AC-based approach is at least as complete as existing algorithms (e.g., do-calculus) for testing classical identifiability, which only assumes the constraint of strict positivity. We use examples to demonstrate the effectiveness of this AC-based approach by showing that unidentifiable causal effects may become identifiable under different types of constraints.

Dependencies among attributes are a common aspect of tabular data. However, whether existing tabular data generation algorithms preserve these dependencies while generating synthetic data is yet to be explored. In addition to the existing notion of functional dependencies, we introduce the notion of logical dependencies among the attributes in this article. Moreover, we provide a measure to quantify logical dependencies among attributes in tabular data. Utilizing this measure, we compare several state-of-the-art synthetic data generation algorithms and test their capability to preserve logical and functional dependencies on several publicly available datasets. We demonstrate that currently available synthetic tabular data generation algorithms do not fully preserve functional dependencies when they generate synthetic datasets. In addition, we also showed that some tabular synthetic data generation models can preserve inter-attribute logical dependencies. Our review and comparison of the state-of-the-art reveal research needs and opportunities to develop task-specific synthetic tabular data generation models. Keywords: Synthetic tabular data, Logical dependencies, Functional dependencies, Generative models 1. Introduction Dependencies among attributes are a common aspect of tabular data. A well-known fact in Database Management Systems is that if one wants to remove redundancies by dividing larger tables into smaller ones (Normalization) [1], one needs tools to identify functional dependencies present among the attributes of the larger table [2]. Preserving functional dependencies in synthetic tabular data is an area that has not been explored. Dependencies exist in both tabular and image data.

Large language models (LLMs) have demonstrated their prowess in generating synthetic text and images; however, their potential for generating tabular data -- arguably the most common data type in business and scientific applications -- is largely underexplored. This paper demonstrates that LLMs, used as-is, or after traditional fine-tuning, are severely inadequate as synthetic table generators. Due to the autoregressive nature of LLMs, fine-tuning with random order permutation runs counter to the importance of modeling functional dependencies, and renders LLMs unable to model conditional mixtures of distributions (key to capturing real world constraints). We showcase how LLMs can be made to overcome some of these deficiencies by making them permutation-aware.

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but limited understanding of the strengths and weaknesses of these models, and the table representations they generate, makes the process of finding a suitable model for a given task reliant on trial and error. There is an urgent need to gain a comprehensive understanding of these models to minimize inefficiency and failures in downstream usage. To address this need, we propose Observatory, a formal framework to systematically analyze embedding representations of relational tables. Motivated both by invariants of the relational data model and by statistical considerations regarding data distributions, we define eight primitive properties, and corresponding measures to quantitatively characterize table embeddings for these properties. Based on these properties, we define an extensible framework to evaluate language and table embedding models. We collect and synthesize a suite of datasets and use Observatory to analyze nine such models. Our analysis provides insights into the strengths and weaknesses of learned representations over tables. We find, for example, that some models are sensitive to table structure such as column order, that functional dependencies are rarely reflected in embeddings, and that specialized table embedding models have relatively lower sample fidelity. Such insights help researchers and practitioners better anticipate model behaviors and select appropriate models for their downstream tasks, while guiding researchers in the development of new models.