Study estimates heterogeneous principal causal effects with binary treatments and intermediate variables.
problem Estimating subgroup effects within strata defined by potential values of an intermediate variable.
method Proposes a framework for estimating and forming confidence intervals for heterogeneous principal causal effects under principal ignorability assumption. Develops several estimators with varying robustness properties.
result Established large-sample theory and analyzed bias contributions of each approach.
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspe…
Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely the adjoint representation and the left (logarithmic) differential. The main res…
Study identifies and estimates treatment effect heterogeneity within principal stratification subpopulations.
problem Causal inference with intermediate outcomes and treatment effect heterogeneity.
method Proposes a novel doubly cross-fit doubly robust machine learner to efficiently learn conditional principal causal effects under principal ignorability.
result Demonstrates informative patterns of treatment effect heterogeneity within the always-survivor subpopulation in an acute lung injury trial.
Direct contextual policy search methods learn to improve policy parameters and simultaneously generalize these parameters to different context or task variables. However, learning from high-dimensional context variables, such as camera images, is still a prominent problem in many real-world tasks. A naive application o…
Unified method learns latent spaces from labeled data.
problem Identifying low-dimensional latent structures in high-dimensional data.
method Nonlinear multiple-response regression within an index model context.
result Unified method offers better interpretability and reduced computational complexity.
Estimates disease prevalence using non-ignorable missing data in health surveys.
problem Estimating disease prevalence in non-representative samples with non-ignorable missing data.
method Connects auxiliary proxy variable framework to label shift setting, uses high-dimensional covariates without generative models.
result Fails to account for non-ignorable missingness can lead to significant misestimations.
A new method for analyzing shapes using FDA techniques.
problem Statistical shape analysis of deformed contours.
method Functional Data Analysis (FDA) with basis expansion and principal component analysis.
result Successfully identifies deformation parameters and captures contour distributions.
The paper clarifies the distinction between CATE and ITE under ignorability assumptions.
problem Confusion between CATE and ITE hinders personalized effect estimation.
method Clarifies the distinction between CATE and ITE under ignorability assumptions.
result CATE and ITE are not necessarily the same under ignorability assumptions.
Operating with ignorance is an important concern of the Machine Learning research, especially when the objective is to discover knowledge from the imperfect data. Data mining (driven by appropriate knowledge discovery tools) is about processing available (observed, known and understood) samples of data aiming to build …
Estimates CATE under hidden confounding, accounting for bias and ignorance.
problem Learning CATE from high-dimensional data with unobserved confounders introduces bias and ignorance.
method Parametric interval estimator that accounts for hidden confounding and underrepresented samples.
result Estimator converges to tight bounds on CATE when there may be unobserved confounding.
Ranked data appear in many different applications, including voting and consumer surveys. There often exhibits a situation in which data are partially ranked. Partially ranked data is thought of as missing data. This paper addresses parameter estimation for partially ranked data under a (possibly) non-ignorable missing…
Algorithm optimizes lockdown policies balancing health and economy.
problem Balancing health and economic impacts of lockdowns during pandemics.
method Reinforcement learning to automatically compute lockdown policies.
result Algorithm learns optimal lockdown policies from disease and population data.
Noise-ignorant empirical risk minimization achieves state-of-the-art performance on noisy data.
problem Learning with noisy labels in multi-class classification problems.
method Introducing relative signal strength (RSS) to quantify transferability and applying Noise Ignorant Empirical Risk Minimization (NI-ERM).
result NI-ERM achieves state-of-the-art performance on CIFAR-N data challenge.
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performa…
A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this…
We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation ti…
Bayesian neural networks ignore data in infinite units limit.
problem Pathological behavior of posterior in over-parameterized networks.
method Mean-field variational inference in infinite hidden units limit.
result Posterior mean converges to zero, ignoring data.
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
problem Generalized principal bundles and connections in field theories.
method Local coordinate transformation laws and horizontal lifts.
result Generalized principal connections are associated to Lie group fiber bundle connections.
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and…
Introduces principal fairness for fair decision-making.
problem Discrimination among similarly affected individuals.
method Uses principal stratification from causal inference.
result Explicitly accounts for decision impacts, not just protected attributes.
Study of semi-principal bundles using group actions and wreath products.
problem Understanding bundles with fibers as free G-spaces. method Defining semi-principal bundles, bases, and frame bundles; using wreath products and functors.
result Semi-principal bundles can be retracted to principal bundles, preserving parallel transport.
The paper classifies and determines properties of specific hypersurfaces in complex hyperbolic quadrics.
problem Analyzing Hopf hypersurfaces with constant principal curvatures in complex hyperbolic quadrics.
method Classification and determination of principal curvatures for hypersurfaces with different numbers of distinct curvatures.
result Classification and determination of principal curvatures for Hopf hypersurfaces with up to four distinct values.
Study on discrete surfaces with constant principal curvature for nanocarbon applications.
problem Understanding discrete geometry properties of nanocarbon materials.
method Developed discrete surface theory on 3-ary oriented trees, defined discrete principal directions, constructed examples of discrete CPC surfaces.
result Construction of discrete constant principal curvature surfaces, including discrete CPC tori.
The paper introduces a method for detecting principal communities and embedding vertices.
problem Detecting and embedding vertices in graphs with community structure.
method Principal graph encoder embedding method that detects principal communities and produces vertex embeddings.
result The method successfully detects principal communities and produces accurate vertex embeddings.
We enumerate all the principal congruence link complements in S3, there by answering a question of W. Thurston. Related articles: "Technical Report: All Principal Congruence Link Groups" (arXiv:1902.04722), "All Known Principal Congruence Links" (arXiv:1902.04426).
A study on how a principal can incentivize an agent to make better decisions in a repeated game.
problem Optimizing a principal's utility in a misaligned principal-agent bandit game.
method Developed nearly optimal learning algorithms for the principal's regret in multi-armed and linear contextual settings.
result The principal can iteratively learn an incentive policy to maximize her total utility.
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
The paper solves the Integration Problem for principal connections.
problem Describing discrete connections associated with a principal connection.
method Using the Lie or derivative functor to induce connections on the principal bundle.
result For flat principal connections, the Integration Problem has a unique solution among flat discrete connections.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admi…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of principal components. We present a gradient ascent algorithm to solve the problem. Fo…
Holonomies match for higher local systems and principal 2-bundles.
problem Matching holonomies for higher local systems and principal 2-bundles.
method Higher Riemann-Hilbert correspondence and principal 2-bundles.
result Holonomies coincide for both formalisms.
Study on isoparametric and constant-curvature hypersurfaces in Finsler spaces.
problem Characterizing and constructing hypersurfaces with specific curvature properties in Finsler geometry.
method Analyzing isoparametric and constant-curvature hypersurfaces on Randers manifolds.
result Construction of a conformally flat Randers manifold with nonisoparametric hyperplanes of constant curvatures.
PCHAL and PCHAR use principal components to speed up HAL and HAR methods.
problem Computational infeasibility in high dimensions for HAL and HAR.
method Outcome-blind principal component reduction of HAL basis.
result Empirical performance comparable to HAL and HAR, with computational gains.
Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.
problem Discretizing curvature line surfaces on square lattices.
method Showed principal binets as a multi-dimensional consistent system.
result Principal binets generalize to higher-dimensional square lattices and are integrable.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group on a groupoid.
In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative de…
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a connection of the differential equations for these curvature lines and real Ricc…
Defines hybrid systems on principal bundles and studies impact effects.
problem Understanding impact effects in hybrid mechanical systems.
method Defines hybrid systems on principal bundles, studies underlying geometry, and finds conditions for impact preservation.
result Conditions for preservation of both exterior and interior impacts by mechanical connections.
A new metric-based principal curve method learns 1D manifolds from spatial data.
problem Learning 1D manifolds from spatial data.
method Metric-based Principal Curve (MPC) approach.
result The method effectively learns the shape of 1D manifolds from synthetic and real datasets.
Study behavior of curvatures near singular points of frontals.
problem Understanding frontals near singular points.
method Investigate principal curvatures and vectors near singular points of frontals.
result Extend Ribaucour transformations to frontals with singular points.
Let X be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let G be a connected complex reductive affine algebraic group equipped with a real form σG. We define pseudo-real principal G--bundles on X; these are generalizations of re…
PFs and iPFs learn principal manifolds for efficient density estimation.
problem Understanding the geometric structure of normalizing flows.
method Characterize flows using principal manifolds and contours.
result PFs and iPFs can learn principal manifolds and perform density estimation.
In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found 'lines and planes of closest fit to system of points'. The famous k…
A principal pair consists of a holomorphic principal G-bundle together with a holomorphic section of an associated Kaehler fibration. Such objects support natural gauge theoretic equations coming from a moment map condition, and also admit a notion of stability based on Geometric Invariant Theory. The Hitchin--Kobaya…