arXiv research

Geometric duality connects graph isomorphism and knot equivalence.

Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.

The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.

The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditi…

The neural tangent kernel equivalence theorem fails in practice.

Study tackles causal structure learning in linear models with unobserved variables and measurement error.

Study compares two knot pairings and their equivalence.

New approach to neural networks by incorporating observation noise and arbitrary prior means.

Characterizes causal structure dominance for latent variables.

Paper designs energy-based controllers and observers for complex systems.

This work uses a scalable approach to identify partially observed nonlinear systems.

MEC-IP uses IP to efficiently find MECs in BNs from observational data.

The paper develops methods to bound causal effects using Partial Ancestral Graphs.

LGES speeds up causal discovery while maintaining accuracy.

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive t…

Intelligent agents can cope with sensory-rich environments by learning task-agnostic state abstractions. In this paper, we propose an algorithm to approximate causal states, which are the coarsest partition of the joint history of actions and observations in partially-observable Markov decision processes (POMDP). Our m…

Transforms between neural networks using manifold-learning techniques.

Counterfactual fairness not equivalent to demographic parity, finds study.

We shrink confidence sets for equivalent discrete distributions using permutation equivalence.

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

Model identifies causal structure from paired observational and interventional data with unknown soft interventions.

Paper proposes scalable algorithm to estimate intervention targets in linear models.

Right-angled Artin groups are classified based on measure equivalence.

We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed variables, each of which is binary. We consider the consequences of imp…

Kichenassamy's work spans theoretical physics, from relativity to applications.

We discuss theoretical aspects of the product rule for classification problems in supervised machine learning for the case of combining classifiers. We show that (1) the product rule arises from the MAP classifier supposing equivalent priors and conditional independence given a class; (2) under some conditions, the pro…

Trajectories of light rays in a static spacetime are described by unparametrised geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the univ…

Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly i…

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $σ$. A…

A new sampler improves the inference of causal structures from observational data.

Separates estimation and control in risk-sensitive investment problems with partial observation.

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are ``symplectic cobordism equivalent.''

We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the …

Question 2.6 of Bestvina's Questions in Geometric Group Theory asks whether every pair of boundaries of a given CAT(0) group G is cell-like equivalent. The question was posed by Bestvina shortly after the discovery, by Croke and Kleiner, of a CAT(0) group that admits multiple boundaries. Previously, it had been observe…

Paper unifies subspace identification and DMD for dynamical systems.

If $\mathcal{M}=(M,\nabla)$ is an affine surface, let $\mathcal{Q}(\mathcal{M}):=\ker(\mathcal{H}+\frac1{m-1}ρ_s)$ be the space of solutions to the quasi-Einstein equation for the crucial eigenvalue. Let $\tilde{\mathcal{M}}=(M,\tilde\nabla)$ be another affine structure on $M$ which is strongly projectively flat. We sh…

Joyce observed that the Alexander invariant and the medial quandle of a classical knot are equivalent to each other, as invariants. In the present paper, we discuss the rather complicated extension of Joyce's observation to several different medial quandles and reduced (one-variable) Alexander modules associated with c…

Optimizes experiment design for causal structure learning in linear models with cycles.

We study the classification problem of singularities of function-germs with harmonic leading terms of two variables under the right-equivalence. We observe that the multiple actions of Laplacian appear for the classifications of such class of function-germs.

It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are give…

Polynomial algorithm found for alternating link equivalence.

We develop a method to summarize causal models with cycles in cubic time.

MuZero visualizes its internal representations to stabilize planning.

We characterize distributional equivalence in latent-variable models with cycles.

Sequence models quantify uncertainty over latent concepts.

New assumptions help identify causal relationships in data.

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The ge…

A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only up to Markov equivalence, based on conditional independence relations among the v…