Extends knockoff filter for composite null hypotheses in variable selection.
problem Handling composite null hypotheses in variable selection.
method Developed two methods for composite inference with knockoffs: S-OLS and FRPP.
result Proposed heuristic variants of S-OLS outperforming BH procedure for composite nulls.
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this compositional structure is reflected in the the inputs' learned representations. W…
Describes explaining neurons in deep representations using compositional logical concepts.
problem Interpreting neuron behavior in deep neural networks.
method Identifying compositional logical concepts that closely approximate neuron behavior.
result Compositional explanations provide insights into model performance and allow for adversarial example creation.
The paper explores local-correlation models for pricing complex financial contracts.
problem Calibrating synthetic quanto forward contracts and composite options.
method Design on-line calibration procedures for local and stochastic volatility models.
result Calibration performance of local-correlation models compared to simpler approximations.
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all tasks -- both have difficulty with such generalization because they do not leve…
Develops consistent approximations for composite optimization problems.
problem Significant errors in solutions due to approximations in optimization problems.
method Specifies conditions for well-behaved approximations in minimizers, stationary points, and level-sets for a broad class of composite problems.
result Framework of consistent approximations for composite problems, including stochastic, neural-network, and multi-objective optimization.
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
Edgeworth Accountant calculates privacy loss under differential privacy compositions efficiently.
problem Efficiently computing overall privacy loss under composition of private algorithms.
method Analytical approach using f-differential privacy framework and Edgeworth expansion. result Non-asymptotic (ε,δ)-differential privacy bounds with reduced computational cost. Learning compact and interpretable representations is a very natural task, which has not been solved satisfactorily even for simple binary datasets. In this paper, we review various ways of composing experts for binary data and argue that competitive forms of interaction are best suited to learn low-dimensional represe…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…
There is tremendous interest in precision medicine as a means to improve patient outcomes by tailoring treatment to individual characteristics. An individualized treatment rule formalizes precision medicine as a map from patient information to a recommended treatment. A treatment rule is defined to be optimal if it max…
Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In…
We consider a group of mean-variance investors with mimicking desire such that each investor is willing to penalize deviations of his portfolio composition from compositions of other group members. Penalizing norm constraints are already applied for statistical improvement of Markowitz portfolio procedure in order to c…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension p can grow exponentially fast with the sample size n. Our method combines the de-biasing technique with the composite quantile function to construct an estimator that …
Introduces derived Lie n-groupoids with shifted symplectic structures.
problem Defines structures for higher groupoids and their symplectic properties.
method Introduced derived Lie n-groupoids and their shifted symplectic structures, defining shifted lagrangian structures and proving composition well-defined.
result Shows that the framework includes various reduction procedures.
Efficient logistic regression for aggregated data reduces computation time.
problem Inference for logistic regression models is computationally expensive for large datasets.
method Adapted symbolic data analysis to summarise predictor variables into histograms and use composite likelihoods.
result The method achieves comparable classification rates to full data analysis but at lower computational cost.
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
Optimizes portfolios using CPT utility via convex optimization.
problem Maximizing CPT utility in portfolio selection.
method Minorization-maximization (MM) algorithm and convex-concave (CC) procedure.
result Problems can be solved globally and efficiently.
Paper introduces ℓ-DER for regression tasks using morphological operators and convex-concave procedure.
problem Developing a universal approximator for regression tasks.
method Introduces ℓ-DER model, trains it using a convex-concave procedure (CCP) to minimize least-squares. result Outperforms other hybrid morphological models and state-of-the-art approaches.
Improves sampling quality in model composition using MH-like acceptance rule for score-based diffusion models.
problem Inability to apply MH corrections in score-based diffusion models for model composition.
method Introduces a novel MH-like acceptance rule based on line integration of the score function.
result Relative improvements similar to energy-based models without explicit energy parameterization.
Generative Adversarial Networks (GAN) (Goodfellow et al., 2014) are an effective method for training generative models of complex data such as natural images. However, they are notoriously hard to train and can suffer from the problem of missing modes where the model is not able to produce examples in certain regions o…
New method selects better graphs for GGM inference in small sample sizes.
problem Inference of conditional correlations in high-dimensional data with limited samples.
method Composite procedure combining nodewise edge selection and penalised likelihood maximisation.
result Our method produces graphs closer to the true distribution with better KL divergence.
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restri…
Geometry-aware KDE model improves multiclass quantification.
problem Accurately estimating class prevalence for label shift adaptation.
method Log-ratio representations and Aitchison geometry for compositional data, shrinkage regularization.
result Competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines.
Constellation learns group-level visual relationships for abstract reasoning.
problem Learning configurational properties of entire groups of objects.
method Introduces Constellation, a network that learns relational abstractions over static visual scenes.
result Offers a basis for abstract relational reasoning and sensory imagination.
Optimizes loan recovery timing across various portfolios.
problem Comparing and evaluating bank's loan recovery decision rules.
method Simulation-based expert system considering time value of money and costs.
result Threshold optima exist across different risk scenarios and portfolio compositions.
Slot Attention extracts object-centric representations from images.
problem Learning distributed representations that don't capture natural scene composition.
method Slot Attention module interfaces with CNN outputs to produce task-dependent abstract slots.
result Slot Attention enables generalization to unseen compositions.
Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantic…
New test detects differences in heterogeneous datasets.
problem Detecting differences between two samples with unknown heterogeneity.
method Developed a nonparametric testing procedure that handles latent heterogeneity through a composite null.
result The test accurately detects differences in the presence of unknown heterogeneity.
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of th…
Paper develops polynomial approximations for complex probability densities.
problem Approximating high-dimensional concentrated probability densities.
method Tensor-product spectral polynomials and KR rearrangements.
result Efficient approximation of complex densities using composite maps.
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth…
Fast detection of changepoints in linear regression models.
problem Early detection of changes in linear regression models.
method Heavy-weighted CUSUM statistics and composite statistics.
result Effective detection of changepoints regardless of their location.
Develops methods for inference after detecting a change in sequential data.
problem Inference after a detected change in sequential data.
method General framework for constructing confidence sets using only data up to a stopping time.
result First general method for sequential changepoint localization with theoretical guarantees.
Improved diffusion models using energy distillation and sequential Monte Carlo.
problem Training instability and inferior performance in energy parameterized diffusion models.
method Introduced a novel training regime for energy functions through distillation of pre-trained diffusion models, and cast the sampling procedure as a Feynman Kac model.
result Demonstrated improved performance and new sampling techniques.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
The paper constructs new algebraic structures from Lie algebras and ternary Nambu-Lie algebras, leading to Yang-Baxter operators.
problem Constructing new algebraic structures from Lie algebras and ternary Nambu-Lie algebras.
method Using compositions of binary Lie algebras, 3-Lie algebras, and ternary Nambu-Lie algebras, the paper constructs ternary self-distributive objects and Yang-Baxter operators.
result The constructed Yang-Baxter operators are not gauge equivalent to the transposition operator and can be deformed to new solutions.
Study on deep neural networks using branching processes and Mehler's formula.
problem Understanding the mathematical role of activation functions in compositional neural networks.
method Connection between compositional kernels and branching processes via Mehler's formula; new random features algorithm.
result Explicit formulas for eigenvalues of compositional kernels quantify complexity.
We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
This paper proves hyperbolicity of virtual knot compositions.
problem Proving hyperbolicity of virtual knot compositions.
method Exploring the composition of hyperbolic virtual knots.
result Strong lower bounds on the volume of compositions.
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on composite fibred manifolds. In particular, we get the horizontal splitting of the vertic…
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
In arXiv:0707.2151 the authors introduced the theory of local representations of the quantum Teichmüller space TSq (q being a fixed primitive N-th root of (−1)N+1) and they studied the behaviour of the intertwining operators in this theory. One of the main results [Theorem 20, arXiv:0707.2151] …
The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy amplification by sampling where the privacy cost of a single evaluation diminishes quadr…
Model predicts composite structures assembly quality with input uncertainty.
problem Accurate prediction of dimensional deviations and residual stress in composite structures assembly.
method Neural Network Gaussian Process considering input uncertainty.
result NNGPIU model outperforms other methods for nonsmooth, nonlinear responses.