arXiv subjects

Orestis Loukas

Publications and source records attributed to Orestis Loukas.

At least 19 recordsLinked to original sources

arXiv2026

The Boltzmann structure of sampling: Intrinsic $p$-value and its emergent closed-form expression

We consider observables $X$ whose realizations in a sampled dataset are restricted, for example by measurement resolution, to a finite set of distinguishable categories within their possibly infinite theoretical domain. Given the probabilities of observable categories, we study the coarse-grained probability mass of families of possible datasets generated through a forward sampling process. The combinatorial construction induces an intrinsically discrete $p$-value defined directly from the sampling process rather than through additional probabilistic structure on observables. Specifying the sample means of $d+k$ arbitrary functions $g_\alpha(X)$ defines a linear family of datasets whose probability mass is obtained as a weighted sum over integer lattice points contained within the associated polyhedron. To overcome the intractable large-$N$ combinatorics, we derive via saddle-point techniques a density approximating these probability masses in the continuum limit of forward sampling within the multinomial universality class. As a demonstration, we consider conditional sampling, where $d$ structural means are fixed while $k$ means vary over admissible datasets. The information geometry emerging from the saddle-point density, together with the spherical symmetry arising at large $N$ from the intrinsic $p$-value construction, enables efficient computation of the $p$-value in the Laplace approximation via the $\chi^2_k$ distribution. The resulting statistic is given by the semi-analytic expression $2N$ times the Kullback-Leibler divergence between the information projections associated with the corresponding structural and observed linear families. These projections can be computed efficiently via standard numerical routines converging for sufficiently well-behaved sample means.

math.ST↗

arXiv2024

A totally empirical basis of science

Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to hypothesis testing make several assumptions on the data generation process beyond the scientific theory. Most of these assumptions not only remain unmet in realistic datasets, but often introduce unwarranted bias in the analysis. Here, we depart from such restrictive assumptions to propose an alternative framework of total empiricism. We derive the Information-test ($I$-test) which allows for testing versatile hypotheses including non-null effects. To exemplify the adaptability of the $I$-test to application and study design, we revisit the hypothesis of interspecific metabolic scaling in mammals, ultimately rejecting both competing theories of pure allometry.

physics.data-an↗

arXiv2024

On the estimation and interpretation of effect size metrics

Effect size estimates are thought to capture the collective, two-way response to an intervention or exposure in a three-way problem among the intervention/exposure, various confounders and the outcome. For meaningful causal inference from the estimated effect size, the joint distribution of observed confounders must be identical across all intervention/exposure groups. However, real-world observational studies and even randomized clinical trials often lack such structural symmetry. To address this issue, various methods have been proposed and widely utilized. Recently, elementary combinatorics and information theory have motivated a consistent way to completely eliminate observed confounding in any given study. In this work, we leverage these new techniques to evaluate conventional methods based on their ability to (a) consistently differentiate between collective and individual responses to intervention/exposure and (b) establish the desired structural parity for sensible effect size estimation. Our findings reveal that a straightforward application of logistic regression homogenizes the three-way stratified analysis, but fails to restore structural symmetry leaving in particular the two-way effect size estimate unadjusted. Conversely, the Mantel-Haenszel estimator struggles to separate three-way effects from the two-way effect of intervention/exposure, leading to inconsistencies in interpreting pooled estimates as two-way risk metrics.

stat.ME↗

arXiv2023

Eliminating confounder-induced bias in the statistics of intervention

Experimental and observational studies often lead to spurious association between the outcome and independent variables describing the intervention, because of confounding to third-party factors. Even in randomized clinical trials, confounding might be unavoidable due to small sample sizes. Practically, this poses a problem, because it is either expensive to re-design and conduct a new study or even impossible to alleviate the contribution of some confounders due to e.g. ethical concerns. Here, we propose a method to consistently derive hypothetical studies that retain as many of the dependencies in the original study as mathematically possible, while removing any association of observed confounders to the independent variables. Using historic studies, we illustrate how the confounding-free scenario re-estimates the effect size of the intervention. The new effect size estimate represents a concise prediction in the hypothetical scenario which paves a way from the original data towards the design of future studies.

stat.ME↗

arXiv2023

Categorical Distributions of Maximum Entropy under Marginal Constraints

The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic theoretical framework that enables this task ensuring (i) that a categorical distribution of Maximum Entropy under marginal constraints always exists and (ii) that it is unique. The procedure of iterative proportional fitting (IPF) naturally estimates that distribution from any consistent set of marginal constraints directly in the space of probabilities, thus deductively identifying a least-biased characterization of the population. The theoretical framework together with IPF leads to a holistic workflow that enables modeling any class of categorical distributions solely using the phenomenological information provided.

hep-th↗

arXiv2023

Total Empiricism: Learning from Data

Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems in the analysis and interpretation of the results. Instead of trying to fix the model or "correct" the data, we here describe a totally empirical statistical approach that does not rely on ad hoc distributional assumptions in order to overcome many problems in contemporary statistics. Starting from elementary combinatorics, we motivate an information-guided formalism to quantify knowledge extracted from the given data. Subsequently, we derive model-agnostic methods to identify patterns that are solely evidenced by the data based on our prior knowledge. The data-centric character of empiricism allows for its universal applicability, particularly as sample size grows larger. In this comprehensive framework, we re-interpret and extend model distributions, scores and statistical tests used in different schools of statistics.

math.ST↗

arXiv2023

Demographic Parity: Mitigating Biases in Real-World Data

Computer-based decision systems are widely used to automate decisions in many aspects of everyday life, which include sensitive areas like hiring, loaning and even criminal sentencing. A decision pipeline heavily relies on large volumes of historical real-world data for training its models. However, historical training data often contains gender, racial or other biases which are propagated to the trained models influencing computer-based decisions. In this work, we propose a robust methodology that guarantees the removal of unwanted biases while maximally preserving classification utility. Our approach can always achieve this in a model-independent way by deriving from real-world data the asymptotic dataset that uniquely encodes demographic parity and realism. As a proof-of-principle, we deduce from public census records such an asymptotic dataset from which synthetic samples can be generated to train well-established classifiers. Benchmarking the generalization capability of these classifiers trained on our synthetic data, we confirm the absence of any explicit or implicit bias in the computer-aided decision.

cs.LG↗

arXiv2022

Entropy-based Characterization of Modeling Constraints

In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a perpendicular formulation to conventional model building, we start from the linear system of phenomenological constraints and asymptotically derive the distribution over all viable distributions that satisfy the provided set of constraints. The MaxEnt distribution plays a special role, as it is the most typical among all phenomenologically viable distributions representing a good expansion point for large-N techniques. This enables us to consistently formulate hypothesis testing in a fully-data driven manner. The appropriate parametric model which is supported by the data can be always deduced at the end of model selection. In the MaxEnt framework, we recover major scores and selection procedures used in multiple applications and assess their ability to capture associations in the data-generating process and identify the most generalizable model. This data-driven counterpart of standard model selection demonstrates the unifying prospective of the deductive logic advocated by MaxEnt principle, while potentially shedding new insights to the inverse problem.

stat.ME↗

arXiv2019

Self-regularizing restricted Boltzmann machines

Focusing on the grand-canonical extension of the ordinary restricted Boltzmann machine, we suggest an energy-based model for feature extraction that uses a layer of hidden units with varying size. By an appropriate choice of the chemical potential and given a sufficiently large number of hidden resources the generative model is able to efficiently deduce the optimal number of hidden units required to learn the target data with exceedingly small generalization error. The formal simplicity of the grand-canonical ensemble combined with a rapidly converging ansatz in mean-field theory enable us to recycle well-established numerical algothhtims during training, like contrastive divergence, with only minor changes. As a proof of principle and to demonstrate the novel features of grand-canonical Boltzmann machines, we train our generative models on data from the Ising theory and MNIST.

cond-mat.dis-nn↗

arXiv2018

An AdS/EFT correspondence at large charge

Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. In this work we discuss the AdS/CFT correspondence in the regime $Q \gg C_T \gg 1$ where both the EFT and gravity descriptions are valid and stable ($C_T$ being the central charge). We present the observation that the ground state energy as a function of the Abelian charge $Q$ for a simple EFT in some three-dimensional CFT coincides with the expression for the mass of an anti-de Sitter-Reissner-Nordström black hole as a function of its charge. This observation allows us to introduce a dictionary relating CFT, EFT and holographic descriptions. We also find agreement for the higher-derivative corrections on both sides, suggesting a large-$C_T$ expansion on the EFT side.

hep-th↗

arXiv2018

A matrix CFT at multiple large charges

We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show the existence of at least two distinct fixed points of the renormalization group (RG) flow. In particular, the one type of those fixed points manifests itself via tractable deviations in the large-charge expansion from the known predictions in the literature. We demonstrate most of the novel features using mainly the example of the $\text{SU}(4)$ matrix theory to compute the anomalous dimension of the lowest scalar operator with large global charge(s).

hep-th↗

arXiv2017

Tension Between a Vanishing Cosmological Constant and Non-Supersymmetric Heterotic Orbifolds

We investigate under which conditions the cosmological constant vanishes perturbatively at the one-loop level for heterotic strings on non-supersymmetric toroidal orbifolds. To obtain model-independent results, which do not rely on the gauge embedding details, we require that the right-moving fermionic partition function vanishes identically in every orbifold sector. This means that each sector preserves at least one, but not always the same Killing spinor. The existence of such Killing spinors is related to the representation theory of finite groups, i.e. of the point group that underlies the orbifold. However, by going through all inequivalent (Abelian and non-Abelian) point groups of six-dimensional toroidal orbifolds we show that this is never possible: For any non-supersymmetric orbifold there is always (at least) one sector, that does not admit any Killing spinor. The underlying mathematical reason for this no-go result is formulated in a conjecture, which we have tested by going through an even larger number of finite groups. This conjecture could be applied to situations beyond symmetric toroidal orbifolds, like asymmetric orbifolds.

hep-th↗

arXiv2017

Matrix models at large charge

We show that the large-charge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal $SU(3)$ matrix model in 2+1 space-time dimensions at fixed charge and calculate the anomalous dimension and fusion coefficients at leading order in the $U(1)$ charge.

hep-th↗

arXiv2017

Compensating strong coupling with large charge

We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $λ_{\text{eff}}\sim λ^b /Q^{a}$, where $λ$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.

hep-th↗

arXiv2016

Abelian scalar theory at large global charge

We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global $U(1)$ charge in an arbitrary number of dimensions. The ground state $| \upsilon\rangle$ is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around $| \upsilon\rangle$ in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show that the whole construction is stable against quantum corrections, in the sense that any higher derivative couplings to Goldstone's tree-level action are suppressed by appropriate powers of the large charge.

hep-th↗

arXiv2016

Calabi-Yau compactifications of non-supersymmetric heterotic string theory

Phenomenological explorations of heterotic strings have conventionally focused primarily on the E8xE8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16)xSO(16) theory and the related supersymmetric E8xE8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the non-supersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16)xSO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.

hep-th↗

arXiv2016

(MS)SM-like models on smooth Calabi-Yau manifolds from all three heterotic string theories

We perform model searches on smooth Calabi-Yau compactifications for both the supersymmetric E8xE8 and SO(32) as well as for the non-supersymmetric SO(16)xSO(16) heterotic strings simultaneously. We consider line bundle backgrounds on both favorable CICYs with relatively small h_11 and the Schoen manifold. Using Gram matrices we systematically analyze the combined consequences of the Bianchi identities and the tree-level Donaldson-Uhlenbeck-Yau equations inside the Kahler cone. In order to evaluate the model building potential of the three heterotic theories on the various geometries, we perform computer-aided scans. We have generated a large number of GUT-like models (up to over a few hundred thousand on the various geometries for the three heterotic theories) which become (MS)SM-like upon using a freely acting Wilson line. For all three heterotic theories we present tables and figures summarizing the potentially phenomenologically interesting models which were obtained during our model scans.

hep-th↗

arXiv2015

Infinite number of MSSMs from heterotic line bundles?

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by letting their background flux quanta grow without bound. Even though we do not have a general proof, we find that all examples are at the boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which can be thought of as vanishing D-term conditions, cannot be satisfied inside the Kaehler cone unless a growing number of scalar Vacuum Expectation Values (VEVs) is switched on. As they are charged under various line bundles simultaneously, the gauge background gets deformed by these VEVs to a non-Abelian bundle. In general, our physical expectation is that such infinite sets of models should be impossible, since they never seem to occur in exact CFT constructions.

hep-th↗