arXiv subjects

Urmi Ninad

Publications and source records attributed to Urmi Ninad.

16 recordsLinked to original sources

arXiv2026

Learning Causal Structure of Time Series using Best Order Score Search

Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al. 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow-shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. Our experiments on synthetic data show that TS-BOSS is especially effective in high auto-correlation regimes, where it consistently achieves higher adjacency recall at comparable precision than standard constraint-based methods. Overall, TS-BOSS offers a high-performing, scalable approach for time series causal discovery and our results provide a principled bridge for extending sparsity-based, permutation-driven causal learning theory to dynamic settings.

cs.LG↗

arXiv2025

Causal discovery on vector-valued variables and consistency-guided aggregation

Causal discovery (CD) aims to discover the causal graph underlying the data generation mechanism of observed variables. In many real-world applications, the observed variables are vector-valued, such as in climate science where variables are defined over a spatial grid and the task is called spatio-temporal causal discovery. We motivate CD in vector-valued variable setting while considering different possibilities for the underlying model, and highlight the pitfalls of commonly-used approaches when compared to a fully vectorized approach. Furthermore, often the vector-valued variables are high-dimensional, and aggregations of the variables, such as averages, are considered in interest of efficiency and robustness. In the absence of interventional data, testing for the soundness of aggregate variables as consistent abstractions that map a low-level to a high-level structural causal model (SCM) is hard, and recent works have illustrated the stringency of conditions required for testing consistency. In this work, we take a careful look at the task of vector-valued CD via constraint-based methods, focusing on the problem of consistency of aggregation for this task. We derive three aggregation consistency scores, based on compatibility of independence models and (partial) aggregation, that quantify different aspects of the soundness of an aggregation map for the CD problem. We present the argument that the consistency of causal abstractions must be separated from the task-dependent consistency of aggregation maps. As an actionable conclusion of our findings, we propose a wrapper Adag to optimize a chosen aggregation consistency score for aggregate-CD, to make the output of CD over aggregate variables more reliable. We supplement all our findings with experimental evaluations on synthetic non-time series and spatio-temporal data.

stat.ME↗

arXiv2025

Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery

Causal discovery aims to extract qualitative causal knowledge in the form of causal graphs from data. Because causal ground truth is rarely known in the real world, simulated data plays a vital role in evaluating the performance of the various causal discovery algorithms proposed in the literature. But recent work highlighted certain artifacts of commonly used data generation techniques for a standard class of structural causal models (SCM) that may be nonphysical, including var- and R2-sortability, where the variables' variance and coefficients of determination (R2) after regressing on all other variables, respectively, increase along the causal order. Some causal methods exploit such artifacts, leading to unrealistic expectations for their performance on real-world data. Some modifications have been proposed to remove these artifacts; notably, the internally-standardized structural causal model (iSCM) avoids varsortability and largely alleviates R2-sortability on sparse causal graphs, but exhibits a reversed R2-sortability pattern for denser graphs not featured in their work. We analyze which sortability patterns we expect to see in real data, and propose a method for drawing coefficients that we argue more effectively samples the space of SCMs. Finally, we propose a novel extension of our SCM generation method to the time series setting.

cs.LG↗

arXiv2025

SpaceTime: Causal Discovery from Non-Stationary Time Series

Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on geographical characteristics such as ecosystem variability. Existing methods for discovering causal graphs from time series either assume stationarity, do not permit both temporal and spatial distribution changes, or are unaware of locations with the same causal relationships. In this work, we therefore unify the three tasks of causal graph discovery in the non-stationary multi-context setting, of reconstructing temporal regimes, and of partitioning datasets and time intervals into those where invariant causal relationships hold. To construct a consistent score that forms the basis of our method, we employ the Minimum Description Length principle. Our resulting algorithm SPACETIME simultaneously accounts for heterogeneity across space and non-stationarity over time. Given multiple time series, it discovers regime changepoints and a temporal causal graph using non-parametric functional modeling and kernelized discrepancy testing. We also show that our method provides insights into real-world phenomena such as river-runoff measured at different catchments and biosphere-atmosphere interactions across ecosystems.

cs.LG↗

arXiv2024

Causal discovery with endogenous context variables

Causal systems often exhibit variations of the underlying causal mechanisms between the variables of the system. Often, these changes are driven by different environments or internal states in which the system operates, and we refer to context variables as those variables that indicate this change in causal mechanisms. An example are the causal relations in soil moisture-temperature interactions and their dependence on soil moisture regimes: Dry soil triggers a dependence of soil moisture on latent heat, while environments with wet soil do not feature such a feedback, making it a context-specific property. Crucially, a regime or context variable such as soil moisture need not be exogenous and can be influenced by the dynamical system variables - precipitation can make a dry soil wet - leading to joint systems with endogenous context variables. In this work we investigate the assumptions for constraint-based causal discovery of context-specific information in systems with endogenous context variables. We show that naive approaches such as learning different regime graphs on masked data, or pooling all data, can lead to uninformative results. We propose an adaptive constraint-based discovery algorithm and give a detailed discussion on the connection to structural causal models, including sufficiency assumptions, which allow to prove the soundness of our algorithm and to interpret the results causally. Numerical experiments demonstrate the performance of the proposed method over alternative baselines, but they also unveil current limitations of our method.

cs.LG↗

arXiv2023

Invariance & Causal Representation Learning: Prospects and Limitations

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables of interest are latent are largely missing. We assay the connection between invariance and causal representation learning by establishing impossibility results which show that invariance alone is insufficient to identify latent causal variables. Together with practical considerations, we use these theoretical findings to highlight the need for additional constraints in order to identify representations by exploiting invariance.

stat.ML↗

arXiv2023

Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions

The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various assumptions that lead to identifiability of the underlying latent causal variables. A large corpus of these preceding approaches consider multi-environment data collected under different interventions on the causal model. What is common to virtually all of these works is the restrictive assumption that in each environment, only a single variable is intervened on. In this work, we relax this assumption and provide the first identifiability result for causal representation learning that allows for multiple variables to be targeted by an intervention within one environment. Our approach hinges on a general assumption on the coverage and diversity of interventions across environments, which also includes the shared assumption of single-node interventions of previous works. The main idea behind our approach is to exploit the trace that interventions leave on the variance of the ground truth causal variables and regularizing for a specific notion of sparsity with respect to this trace. In addition to and inspired by our theoretical contributions, we present a practical algorithm to learn causal representations from multi-node interventional data and provide empirical evidence that validates our identifiability results.

stat.ML↗

arXiv2023

Projecting infinite time series graphs to finite marginal graphs using number theory

In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past and future and whose edges are repetitive in time, thereby reflecting the assumption of stationary causal relationships. However, most results and algorithms from the causal-graphical-model framework are not designed for infinite graphs. In this work, we develop a method for projecting infinite time series graphs with repetitive edges to marginal graphical models on a finite time window. These finite marginal graphs provide the answers to $m$-separation queries with respect to the infinite graph, a task that was previously unresolved. Moreover, we argue that these marginal graphs are useful for causal discovery and causal effect estimation in time series, effectively enabling to apply results developed for finite graphs to the infinite graphs. The projection procedure relies on finding common ancestors in the to-be-projected graph and is, by itself, not new. However, the projection procedure has not yet been algorithmically implemented for time series graphs since in these infinite graphs there can be infinite sets of paths that might give rise to common ancestors. We solve the search over these possibly infinite sets of paths by an intriguing combination of path-finding techniques for finite directed graphs and solution theory for linear Diophantine equations. By providing an algorithm that carries out the projection, our paper makes an important step towards a theoretically-grounded and method-agnostic generalization of a range of causal inference methods and results to time series.

math.ST↗

arXiv2023

Causal discovery for time series from multiple datasets with latent contexts

Causal discovery from time series data is a typical problem setting across the sciences. Often, multiple datasets of the same system variables are available, for instance, time series of river runoff from different catchments. The local catchment systems then share certain causal parents, such as time-dependent large-scale weather over all catchments, but differ in other catchment-specific drivers, such as the altitude of the catchment. These drivers can be called temporal and spatial contexts, respectively, and are often partially unobserved. Pooling the datasets and considering the joint causal graph among system, context, and certain auxiliary variables enables us to overcome such latent confounding of system variables. In this work, we present a non-parametric time series causal discovery method, J(oint)-PCMCI+, that efficiently learns such joint causal time series graphs when both observed and latent contexts are present, including time lags. We present asymptotic consistency results and numerical experiments demonstrating the utility and limitations of the method.

stat.ME↗

arXiv2023

Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery

Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather unrealistic assumptions. One of these assumptions is homoskedasticity, in other words, a constant conditional variance is assumed. We frame heteroskedasticity in a structural causal model framework and present an adaptation of the partial correlation CI test that works well in the presence of heteroskedastic noise, given that expert knowledge about the heteroskedastic relationships is available. Further, we provide theoretical consistency results for the proposed CI test which carry over to causal discovery under certain assumptions. Numerical causal discovery experiments demonstrate that the adapted partial correlation CI test outperforms the standard test in the presence of heteroskedasticity and is on par for the homoskedastic case. Finally, we discuss the general challenges and limits as to how expert knowledge about heteroskedasticity can be accounted for in causal discovery.

stat.ME↗

arXiv2023

Foundations of Causal Discovery on Groups of Variables

Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or neuroscience. If the group-level causal models are derived from partitioning a micro-level model into groups, we explore the relationship between micro and group-level causal discovery assumptions. We investigate the conditions under which assumptions like Causal Faithfulness hold or fail to hold. Our analysis encompasses graphical causal models that contain cycles and bidirected edges. We also discuss grouped time series causal graphs and variants thereof as special cases of our general theoretical framework. Thereby, we aim to provide researchers with a solid theoretical foundation for the development and application of causal discovery methods for variable groups.

stat.ME↗

arXiv2023

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

physics.data-an↗

arXiv2022

Vector causal inference between two groups of variables

Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based non-parametric approach for inferring the causal relationship between two vector-valued random variables from observational data. Our method employs sparsity estimates of directed and undirected graphs and is based on two new principles for groupwise causal reasoning that we justify theoretically in Pearl's graphical model-based causality framework. Our theoretical considerations are complemented by two new causal discovery algorithms for causal interactions between two random vectors which find the correct causal direction reliably in simulations even if interactions are nonlinear. We evaluate our methods empirically and compare them to other state-of-the-art techniques.

stat.ME↗

arXiv2021

BPS Indices, Modularity and Perturbations in Quantum K-theory

We study a perturbation family of N=2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians. The 3d BPS half-index of the gauge theory is connected to the theory of bilateral hypergeometric q-series, and to modular q-characters of a class of conformal field theories in a certain massless limit. Turning on 3d Wilson lines at torsion points leads to mock modular behavior. Perturbed correlators in the IR regime are computed by determining the UV-IR map in the presence of deformations.

hep-th↗

arXiv2019

Wilson loop algebras and quantum K-theory for Grassmannians

We study the algebra of Wilson line operators in three-dimensional N=2 supersymmetric U(M) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M,N), and its connection to K-theoretic Gromov-Witten invariants for Gr(M,N). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M,N), isomorphic to the Verlinde algebra for U(M), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

hep-th↗

arXiv2018

The Geometry of Gauged Linear Sigma Model Correlation Functions

Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N=(2,2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation functions, which yield differential equations governing the dependence of the gauge theory ground state on the Fayet-Iliopoulos parameters of the gauge theory. For gauge theories with a non-trivial infrared N=(2,2) superconformal fixed point, these differential equations become the Picard-Fuchs operators governing the moduli-dependent vacuum ground state in a Hilbert space interpretation. For gauge theories with geometric target spaces, a quadratic expression in the Givental I-function generates the analyzed correlators. This gives a geometric interpretation for the correlators, their relations, and the differential equations. For classes of Calabi-Yau target spaces, such as threefolds with up to two Kahler moduli and fourfolds with a single Kahler modulus, we give general and universally applicable expressions for Picard-Fuchs operators in terms of correlators. We illustrate our results with representative examples of two-dimensional N=(2,2) gauge theories.

hep-th↗