Unified algorithm for efficient pure exploration using dual variables.
problem Efficiently achieving a specific goal through adaptive experimentation.
method Introducing dual variables to derive optimal allocation conditions, leading to Information-Directed Selection.
result Top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification.
LOVE method estimates factor model entries and structure from sparse data.
problem Estimating factor model entries and structure from sparse data with unknown number of factors and pure variables.
method Adaptive estimation method LOVE that identifies loading matrix A from X = AZ + E.
result The loading matrix A is uniquely defined up to signed permutations with minimal conditions.
Paper relaxes identifiability conditions for causal models with latent variables.
problem Challenges in identifying causal graphical models with latent variables.
method Proposes a double triangular graphical condition for nonparametric measurement models with binary latent variables.
result Guarantees identifiability of the entire causal graphical model under relaxed conditions.
Develops a Bayesian non-parametric approach for signal separation with varying components.
problem Signal separation with varying components across different input locations.
method Augments Gaussian Process Latent Variable Models with weighted sums of pure component signals and incorporates priors for linear weights.
result Framework allows for non-linear variations in signals and incorporates useful priors for linear weights.
Methodology calculates car insurance premiums for partial damage losses.
problem Estimating premiums for partial damage losses in automobile insurance.
method Used generalized linear models to analyze claim frequency and severity.
result Identified key variables influencing claim frequency and severity.
New methods for hyperspectral unmixing handle intra-class variability.
problem Intra-class variability in hyperspectral images.
method Inertia-constrained Pixel-by-pixel NMF (IP-NMF) for handling variability.
result IP-NMF outperforms state-of-the-art methods in real data.
A new geometric approach to quantum mechanics simplifies time-dependent problems.
problem Quantum mechanics ambiguities in time and observer choices.
method Generally covariant phase-spacetime coordinates and geometric flatness condition.
result Quantum mechanics becomes purely geometric and potentially topological.
Estimates joint causal effects using single-variable interventions on nonlinear models.
problem Estimating joint causal effects from single-variable interventions.
method Identifiability result and practical estimator for decomposing causal effects.
result Joint effects can be inferred without joint interventional data for nonlinear additive models.
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…
CIB compresses variables causally, preserving key causal interactions.
problem Constructing causal variable abstractions in complex systems.
method Causal Information Bottleneck (CIB) method, extending IB to include causal structures.
result CIB produces causally interpretable abstractions that accurately capture causal relations.
GNMT uses latent variables to improve machine translation, especially with missing words.
problem Improving machine translation, especially with missing words.
method GNMT adds a latent variable to an encoder-decoder model to capture sentence semantics.
result GNMT achieves competitive BLEU scores and is superior when source sentences are missing words.
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but thei…
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and convergent variational algorithms, such as dual decomposition, exist. In this work,…
New method selects direct causal parents from large sets of variables.
problem Inferring direct causal parents from many variables, especially nonlinear and cyclic.
method One-vs.-the-rest feature selection approach with theoretical guarantees.
result Significant improvements over existing methods.
In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ". The purpose of this paper is to extend such a point of view to differential module…
New method identifies latent causal factors from observational data alone.
problem Identifying latent causal factors without interventions or graphical restrictions.
method Characterization of latent factors in nonlinear causal models with additive Gaussian noise and linear mixing, using a practical algorithm based on solving a quadratic program over observed data.
result Latent causal variables can be identified up to a layer-wise transformation, and further disentanglement is not possible.
Develops a method to identify causal effects in linear models with latent variables.
problem Identifying causal effects in models with latent variables that are not independent.
method A novel graphical criterion and an integer linear program algorithm.
result Sufficient condition for identifying causal effects by rational formulas in the covariance matrix.
AugBagg improves random forest accuracy with added noise variables.
problem Improving model accuracy with random forest.
method AugBagg procedure using additional noise variables.
result Out-of-sample predictive accuracy improved with AugBagg.
The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However, it is also clear that a purely relevance-oriented criterion could lead to selec…
Paper introduces DP methods for high-dimensional variable selection.
problem Sparse variable selection in high-dimensional learning.
method Pure differentially private estimators using Integer Programming.
result Achieves state-of-the-art empirical support recovery.
Spacetimeformer learns spatiotemporal relationships from data alone.
problem Forecasting multivariate time series with distinct spatial relationships.
method Transformers with dynamic graph connections learning interactions between space, time, and value.
result Competitive results on various time series prediction benchmarks.
New quantum states capture more information, enabling advanced processing tasks.
problem Quantum information processing challenges with limited statistical information.
method Introducing Random-Coefficient Pure States (RCPS) and exploiting their higher-order statistics.
result RCPS provide richer information than density operators, enabling new quantum tasks.
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fix…
Paper compares machine learning models for food authenticity.
problem Determining correct food labelling from NIR spectroscopic data.
method Applied and compared various classification, dimension reduction, and variable selection approaches to NIR datasets of meat, olive oil, and honey samples.
result Partial least squares outperformed other approaches in classifying food authenticity.
The paper classifies curves in dual affine and Lorentz-Minkowski planes with constant curvature.
problem Classifying curves with constant curvature in dual affine and Lorentz-Minkowski planes.
method Investigation of invariants under equiaffine transformations and explicit equations for curves with constant curvature.
result Curves with constant curvature in dual affine and Lorentz-Minkowski planes are classified.
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
Investigates curvature properties of special pure radiation metrics.
problem Analyzes the curvature of specific pure radiation spacetimes.
method Examines curvature properties of special pure radiation metrics using conformal relations and tensor analysis.
result Shows that special pure radiation spacetimes are semisymmetric, Ricci simple, and R-space.
A new invariant for pure braids is defined and shown not to be trivial.
problem Defining a non-trivial invariant for pure braids.
method Using recoupling theory to define a representation of the pure braid group.
result The defined representation is not trivial.
Characterizes optimal-speed quantum state evolution Hamiltonians.
problem Optimal-speed unitary time evolution of pure and quasi-pure quantum states.
method Construction of the manifold of pure states and isometry with flag manifold, characterization of equigeodesic vectors.
result Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of the flag manifold.
The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, as well as some differential results. Furthermore, the freedom in the…
The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's vector fields, Hodge star operator, integral forms, co-differential and connection on…
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X,D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it wi…
Researchers develop Malliavin calculus for signatures, simplifying option Greeks computation.
problem Lack of tractability and explicit representations in Malliavin calculus.
method Focus on finite linear combinations of time-extended Brownian motion signatures, derive explicit formulas for Malliavin derivative, and compute Greeks for path-dependent options.
result Closed-form expressions for classical operators of Malliavin calculus, providing algebraic formulations.
A new method purifies interaction effects in models to improve interpretability.
problem Interaction effects can be misinterpreted as separate main effects, complicating model interpretation.
method Proposes pure interaction effects and a Functional ANOVA decomposition algorithm to identify and isolate interaction effects.
result Identifies and separates interaction effects from main effects, showing large disparities in model interpretation.
The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffia…
A fast algorithm for counting Markov equivalent DAGs and designing experiments.
problem Counting Markov equivalent DAGs and designing experiments efficiently.
method LazyIter algorithm for efficient iteration over MECs, utilizing intervention results.
result Significant reduction in time complexity for sparse graphs (O(n)).
SMT-EX enhances SMT for explaining surrogate models of mixed-variable design problems.
problem Making decisions and understanding complex systems using surrogate models of mixed-variable design problems.
method Integrates explainability techniques into SMT, including Shapley Additive Explanations, Partial Dependence Plot, and Individual Conditional Expectations.
result Demonstrates versatility in addressing diverse problem characteristics.
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, …
The CN matrix of a pure braid projection is characterized and applied.
problem Understanding the structure of CN matrices for braid projections.
method Discussion and characterization of patterns and specific matrices.
result Characterization of CN matrix of a pure 6-braid projection and related matrices.
Corrects earlier work on surface orbifold pure braid groups.
problem Proving a four-term exact sequence for surface orbifold pure braid groups.
method Analyzes surface orbifold pure braid groups for all genus ≥ 1, 2D orientable orbifolds with cone points.
result Proves a four-term exact sequence for surface orbifold pure braid groups.
In this mostly survey paper, we investigate the resonance varieties, the lower central series ranks, and the Chen ranks, as well as the residual and formality properties of several families of braid-like groups: the pure braid groups Pn, the welded pure braid groups wPn, the virtual pure braid groups vPn, as w…
Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that…
Study automorphisms of pure braid groups on sphere homotopy groups.
problem Understanding automorphisms' effect on sphere homotopy groups.
method Examined Delta-group structure, proved invariance of cycle and boundary groups, computed action for few strands.
result Induced action of all automorphisms of pure braid groups on sphere homotopy groups.
Summary of pure cactus groups and circle points.
problem Understanding pure cactus groups and configuration spaces.
method Summarizes previous work on the topic.
result Summary of results from previous papers and thesis.
We find finite presentations for the automorphism group of the Artin pure braid group and the automorphism group of the pure braid group associated to the full monomial group.
In this paper it is proved that the pure braided Thompson's group BF admits a bi-order, analog to the bi-order of the pure braid groups.
New method detects latent common causes from observational data.
problem Detecting latent common causes in observational data.
method Modified causal discovery algorithms to detect latent common causes.
result Successfully detects latent common causes in various noise regimes and real data.
Derives equations for forced systems using variational methods.
problem Designing high-order integrators for forced Lagrangian systems.
method Duplicating variables and applying variational order to forced systems.
result Characterization of method order using variational order of duplicated system.