New algorithm uses conditionally invariant components to improve domain adaptation performance.
problem Improving domain adaptation performance when source and target data distributions differ.
method Conditionally invariant components (CICs) and importance-weighted conditional invariant penalty (IW-CIP) algorithm.
result New algorithm provides target risk guarantees and addresses label-flipping features.
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data p…
New method improves deep CCA by modeling private components conditionally independent of common factors.
problem Discovering latent co-variation in multiview datasets with weak common factors.
method Proposes a novel formulation that models private components conditionally independent of common factors.
result Validates the approach with synthetic and real datasets, showing improved identification of common factors.
New analysis identifies key factors in wildfire-generated thunderstorms.
problem Understanding the causes of pyrocumulonimbus (pyroCb) storms.
method Invariant Causal Prediction, conditional independence test, greedy-ICP search algorithm.
result Identified seven causal predictors for pyroCb formation.
SFB uses stable features to adapt unstable ones for better performance.
problem Improving classifier performance on out-of-distribution data by leveraging stable features.
method SFB learns a predictor that separates stable and unstable features, then adapts unstable predictions using stable predictions.
result SFB can learn an asymptotically-optimal predictor without test-domain labels.
We describe a mechanism by which artificial neural networks can learn rapid adaptation - the ability to adapt on the fly, with little data, to new tasks - that we call conditionally shifted neurons. We apply this mechanism in the framework of metalearning, where the aim is to replicate some of the flexibility of human …
Clustering evaluation measures are frequently used to evaluate the performance of algorithms. However, most measures are not properly normalized and ignore some information in the inherent structure of clusterings. We model the relation between two clusterings as a bipartite graph and propose a general component-based …
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can detect and we propose a computationally efficient method based on semidefinite prog…
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way to efficiently construct them. For the stochastic optimization problems that dom…
Analyzes geodesic lengths in sparse networks, deriving a distribution.
problem Understanding connectivity and robustness in networked systems.
method Analytic derivation of geodesic length distribution in sparse networks.
result Simple closed-form expression for geodesic length distribution.
We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor…
We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with condition…
New invariants lift Milnor invariants for 3-component links.
problem Classifying 3-component links using Milnor invariants.
method Defined and proved invariants γk(L), introduced h(L), and showed their equivalence. result Invariants γk(L) lift certain Milnor invariants and are invariant under weak cobordism. Innovates a three-component link homotopy invariant.
problem Classifying three-component link maps up to homotopy.
method Developed tools and invariants for distinguishing three-component link maps.
result Found three-component link maps that are not homotopic.
We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show th…
One of the major shortcomings of variational autoencoders is the inability to produce generations from the individual modalities of data originating from mixture distributions. This is primarily due to the use of a simple isotropic Gaussian as the prior for the latent code in the ancestral sampling procedure for the da…
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
DPA autoencoders learn data distribution and intrinsic dimensionality with guarantees.
problem Learning data distribution and intrinsic dimensionality in unsupervised learning.
method Combines distributionally correct reconstruction with principal-component-like interpretability.
result Exact theoretical guarantees on disentangling factors of variation and intrinsic dimensionality.
CW-Gen models improve probabilistic time series forecasting by incorporating prior information.
problem Challenges in probabilistic forecasting of multivariate time series due to non-stationarity, inter-variable dependencies, and distribution shifts.
method CW-Gen framework that incorporates prior information through conditional whitening. JMCE learns conditional mean and covariance, improving sample quality.
result CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches.
Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to accou…
Extends Benard-Conway invariant to all two-component links.
problem Counting irreducible SU(2) representations for two-component links.
method Counting irreducible SU(2) representations with fixed meridional traces.
result Invariant equals symmetrized multivariable link signature for (2, 2n)-torus links.
Study minimax optimal RL in factored MDPs with bonus exploration.
problem Optimal reinforcement learning in episodic factored MDPs.
method Proposes two model-based algorithms with bonus exploration for minimax optimal regret.
result Achieves minimax optimal regret guarantees for rich factored structures.
Develops CLDS models to model neural activity with nonlinear dynamics.
problem Complex, nonlinear dynamics in neural population activity.
method Conditionally Linear Dynamical System (CLDS) models using Gaussian Process (GP) priors.
result CLDS models can perform well even in data-limited conditions.
Defines new link-homotopy invariants using Milnor's higher order link invariants.
problem Link-homotopy invariants for link maps of multiple components.
method Uses Milnor's higher order link invariants and combinatorial theory of cut-diagrams.
result Provides practical algorithms to compute these invariants and detects families of examples.
A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a …
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
Introduces CSLC models to bridge deep generative models and classical algorithms.
problem Mode collapse and memorization issues in deep generative models and restrictive assumptions in classical algorithms.
method Introduces conditionally strongly log-concave (CSLC) models, factorizing data distribution into strongly log-concave conditional distributions.
result Efficient parameter estimation and sampling algorithms with theoretical guarantees for non-log-concave data distributions.
Providing meaningful privacy to users of location based services is particularly challenging when multiple locations are revealed in a short period of time. This is primarily due to the tremendous degree of dependence that can be anticipated between points. We propose a Rényi differentially private framework for boundi…
The paper extends CF-moves to classify virtual links of any number of components.
problem Classifying virtual links using CF-moves.
method Extending CF-moves to classify virtual links of arbitrary number of components using the virtual linking number and invariants.
result Classification of 3-component even virtual links up to CF-moves.
Modeling financial returns as conditionally independent random variables explains power-law tails.
problem Understanding the distribution of financial returns and their relation to volatility.
method Assuming returns are conditionally independent given volatility, which varies randomly over time.
result Returns distribution can be described by the sum of conditionally independent random variables, showing scaling and power-law tails.
GT-PCA improves PCA for image and time series data.
problem Lack of robustness to transformations in PCA.
method GT-PCA is a neural network that estimates components invariant to specific transformations.
result GT-PCA outperforms alternative methods in synthetic and real data experiments.
The paper develops a new simulation technique for estimating conditional expectations in financial models.
problem Estimating conditional expectations in financial models with expensive simulation of endogenous variables.
method Introduces a hierarchical simulation scheme with oversimplified defaults to address variance issues.
result The hierarchical simulation technique significantly improves the success of neural net regression for conditional expectation estimation.
The article calculates asymptotic expansions for quantum invariants from surgeries on Whitehead link components.
problem Calculating quantum invariants for 3-manifolds resulting from surgeries on Whitehead link components.
method Asymptotic expansion of relative Reshetikhin-Turaev and Turaev-Viro invariants.
result Asymptotic formulas for both invariants are derived.
We construct a geometric, real analytic parametrization of the Hitchin component Hit_n(S) of the PSL_n(R)-character variety R_{PSL_n(R)}(S) of a closed surface S. The approach is explicit and constructive. In essence, our parametrization is an extension of Thurston's shear coordinates for the Teichmueller space of a cl…
In this paper we show some properties of triangle invariants and shearing invariants of PSL(n,R)-Fuchsian representations. Moreover, using the Bonahon-Dreyer parameterization, we show that the Fuchsian locus of Hitchin components corresponds to a slice.
Study improves conformal prediction for missing covariate data.
problem Uncertainty quantification with missing covariate values.
method Generalized conformalized quantile regression framework, missing data augmentation.
result Improved prediction intervals valid conditionally to missing data patterns.
The paper studies invariants of surfaces in the 3-sphere using handlebody-links.
problem Understanding invariants of surfaces in the 3-sphere.
method Using Heegaard splittings and G-families of quandles to construct invariants. result Invariants can distinguish certain surfaces in the 3-sphere.
The Kreck-Stolz s-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being defined only under restrictive topological conditions. The aim of this paper is t…
Khovanov homology invariant under Conway mutation.
problem Invariance of Khovanov homology under specific transformations.
method Strong geography restrictions and homological mirror symmetry.
result Classification of components of a Khovanov multicurve invariant.
Optimizes mixture models without parametrizing distributions using tensor decomposition.
problem Estimating conditionally-independent mixture models in high dimensions.
method Alternating least squares optimization scheme for tensor decomposition.
result Competitive performance and applicability to various models and applications.
A new optimizer DDC improves deep learning models by respecting symmetries.
problem Deep networks' loss is invariant to continuous symmetries, leading to optimization issues.
method DDC builds a Dead-Direction Conditioner that lifts a base optimizer into a G-equivariant one, preserving the quotient geometry.
result DDCAdam and DDCMuon outperform standard optimizers in various tasks, improving validation-train loss gaps and learning dynamics.
New algebraic structures help categorify link invariants.
problem Classifying and distinguishing links and virtual links.
method Introducing mc-biquandles and categorifying homsets.
result New link invariants defined via mc-biquandle coloring quivers.
We study Heegaard Floer homology and various related invariants (such as the h-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the h-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…
Study on string links invariant under associator choice and Grothendieck--Teichmüller group action.
problem Independence of Kontsevich invariant under associator choice for 2-component string links.
method Investigation of Kontsevich invariant for 2-component string links and action of Grothendieck--Teichmüller group.
result Non-trivial action of Grothendieck--Teichmüller group on algebra of 2-component string links.
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penal…