A new ensemble learning method called Residual Likelihood Forests improves performance and reduces model size.
problem Improving machine learning classification performance with compact models.
method Sequential optimization of conditional likelihoods in a boosting-like framework, combining multiplicatively.
result Significant performance improvements and reduced model size compared to other ensemble methods.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual nois…
Study on likelihood functions, associative equations, and Frobenius manifolds.
problem Maximum likelihood estimation and associativity equations in statistical models.
method Analyzes the cone of concentration matrices, log-likelihood function, and Frobenius manifolds.
result Maximum likelihood degree is indexed by components of Frobenius residuals.
Alternative to likelihood-based LSNM model selection, residual independence testing is more robust to noise misspecification.
problem Cause-effect inference in location-scale noise models with misspecified noise distributions.
method Residual independence testing as an alternative to likelihood-based model selection.
result Residual independence testing is more robust to noise misspecification.
Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorized likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This approximation is clearly limited as demonstrated by observing a residual image from a VAE …
Two methods are proposed to filter correlations in DCC-GARCH residuals for foreign exchange rates.
problem Filtering correlations in DCC-GARCH residuals for accurate foreign exchange rate prediction.
method Two approaches: estimating correlation matrix as a parameter and using eigenvalue decomposition.
result The DCC-GARCH residual can be almost independent using these methods.
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple …
We speed up Gaussian process cross-validation calculations and improve model diagnostics.
problem Efficiently calculating cross-validation residuals and their covariances in Gaussian processes.
method Generalized fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting covariance structures.
result Correcting for residual covariances in cross-validation improves back to Maximum Likelihood Estimation.
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situa…
New diagnostic method detects misspecified models in inverse PDE problems.
problem Misleading residual-norm diagnostics in inverse PDE problems.
method Structure-sensitive sequential diagnostic using e-processes.
result Rejects fitted models that produce biased predictions.
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data v…
New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.
A robust Gaussian process model using Huber likelihood for outlier resistance.
problem Outliers in observational data sets affect Gaussian process regression's robustness.
method Proposes a Gaussian process model with Huber likelihood and weights based on projection statistics.
result Demonstrates improved statistical efficiency and robustness to outliers.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
Optimizes AIS hyperparameters for efficient marginal likelihood estimation.
problem Limited computation budget affects AIS performance.
method Flexible intermediary distributions defined by residual density, parameter sharing, and fix linear schedule.
result Optimized-Path AIS reduces sampling iterations and improves performance.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
The paper improves random forest models for non-Gaussian responses.
problem Improving random forest models for non-Gaussian responses.
method Extends boosting random forests to model exponential family responses using residuals and weights.
result Generalized boosted forests reduce bias and provide conservative confidence intervals.
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…
DeRegiME forecasts with regime structure, improving probabilistic predictions across various time series.
problem Probabilistic forecasting discards residual uncertainty, and distribution shifts are hard to capture.
method DeRegiME uses a sparse variational Gaussian process with a nonstationary regime-mixing kernel to separate latent uncertainty regimes.
result DeRegiME improves NLPD by 20.3% on average across benchmarks, with gains on CRPS and MSE.
Paper explores connections between loss functions and consistency in binary classification and regression.
problem Consistency in binary classification and regression applications.
method Characterization of conformable loss functions and derivation of a new Huber-type loss function.
result Margin-based loss functions are equivalent to loss functions of squared standardized logistic regression residuals.
We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size …
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
NVAE improves VAE performance on large image datasets.
problem Improving variational autoencoder performance for large image datasets.
method Deep hierarchical VAE with depth-wise separable convolutions and batch normalization, residual parameterization of Normal distributions, and spectral regularization.
result NVAE achieves state-of-the-art results on MNIST, CIFAR-10, CelebA 64, and CelebA HQ datasets.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to predict a full Gaussian covariance matrix for each reconstruction, which permits …
Mammographic breast density, a parameter used to describe the proportion of breast tissue fibrosis, is widely adopted as an evaluation characteristic of the likelihood of breast cancer incidence. In this study, we present a radiomics approach based on residual learning for the classification of mammographic breast dens…
Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, resp…
Graph neural networks often assume vertex labels are independent, but we show this is rarely true and propose a method to improve predictions.
problem Graph neural networks often assume vertex labels are conditionally independent given their neighborhood features, which is rarely true.
method We model the joint distribution of residuals on vertices with a parameterized multivariate Gaussian and estimate parameters by maximizing the marginal likelihood of the observed labels.
result Our method achieves substantially higher accuracy than competing baselines and can be interpreted as the strength of correlation among connected vertices.
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
RECLAIM discovers causal graphs in cyclic, noisy systems.
problem Discovering causal relationships in cyclic, noisy systems.
method RECLAIM uses EM with residual normalizing flows to handle cycles and noise.
result RECLAIM effectively discovers causal graphs in both synthetic and real-world datasets.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
This paper proposes a new RV prediction model using neural distributional transformation and co-training.
problem Predicting skewed and fat-tailed realized volatility (RV) is challenging.
method The paper uses a neural distributional transformation and co-training to predict RV. It jointly trains the transformation and prediction model using a maximum-likelihood objective function.
result The proposed method significantly outperforms other methods on a dataset of 100 stocks.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…
FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.
problem Learning a separate flow for every parameter configuration is intractable.
method Factorizable Normalizing Flows (FNFs) represent the parameter-dependent density as a fixed flow for a reference configuration and a learnable polynomial transformation factorized over parameters.
result FNFs enable the recovery of the combined effect of multiple parameters without sampling their joint space, providing a scalable and interpretable solution.
Every non-trivial knot group is fully residually perfect.
problem Understanding the residual properties of knot groups.
method Analyzing the residual properties of knot groups using group theory.
result Every non-trivial knot group is fully residually perfect.
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
Method estimates bivariate causal models using normalising flows and variational Gaussian process regression.
problem Lack of explainability in AI models, especially in causal mechanisms.
method Combination of normalising flows for density estimation and variational Gaussian process regression for post-nonlinear models.
result Method better explains cause-effect pairs than simple additive noise models.
This paper presents a sequential method to identify the topological ordering of causal DAGs using likelihood ratio scores.
problem Identifying the causal relationships in a data mining scenario with ambiguity of causal directions.
method A general sequential sorting procedure that orders variables one at a time, starting at root nodes, followed by children of the root nodes, and so on until completion. Simple likelihood ratio scores are used to decide the next node to append to the current partial ordering.
result The population version of the procedure provably identifies a true ordering of the underlying DAG under mild assumptions.
Let p be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually p. Let M=M3 be a virtually fibered 3-manifold. It is well-known that G=π1(M) is residually solvable and even residually finite solvable. We prove that G is always virtually residually p…
Researchers identify critical protein residues using advanced graph theory.
problem Identifying essential residues in proteins for function.
method Learning Random Geometric Graphs (RGG) with Cramer's V correlation and organic thresholding.
result Advanced RGG methods accurately identify critical residues compared to existing techniques.
Defines Wodzicki residue using groupoids and fibered distributions.
problem Defining and understanding the Wodzicki residue in noncommutative geometry.
method Using groupoid language and filtered manifolds, defining the residue and showing its properties.
result The groupoidal residue is a trace on pseudodifferential operators and matches the usual residue in certain cases.
In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this …