Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
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.
Efficient binary sampling method for global optimization of univariate functions with low regret.
problem Global optimization of univariate loss functions.
method Binary sampling approach to circumvent hard-to-determine query points in traditional methods.
result At most Llog(3T) and 2.25H regret for L-Lipschitz continuous and H-Lipschitz smooth functions respectively. Study active learning of PTFs with derivative access.
problem Active learning of polynomial threshold functions (PTFs).
method Algorithm for active learning degree-d univariate PTFs with derivative access. result Computational efficient algorithm for active learning degree-d univariate PTFs. New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
Shallow neural networks can represent polynomials efficiently.
problem Representing polynomials using shallow neural networks.
method Using shallow neural networks of width 2(R+d)d to represent d-variate polynomials of degree R. result Derives minimax optimal convergence rate for shallow networks to unknown univariate regression functions.
Proposes a method to partition univariate data into unimodal subsets.
problem Partitioning univariate multimodal data into unimodal subsets.
method Recursive splitting around valley points of the data density using properties of critical points on the convex hull of the ecdf plot.
result Obtains a hierarchical statistical model of the initial dataset as a mixture of UMMs.
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
AI learns to classify and represent univariate distributions in a 2D latent space.
problem Classifying and representing univariate empirical distributions.
method Unsupervised beta variational autoencoder (beta-VAE) to separate and represent distributions in a 2D latent space.
result The latent space representation separates distributions of different shapes while overlapping similar ones.
Meta algorithm solves multivariate optimization using univariate optimizers.
problem Multivariate global optimization problems.
method Meta algorithm combining univariate global optimizers.
result Meta algorithm provides robust regret guarantees.
Dynamic functional time-series methods improve forecast accuracy for foreign exchange implied volatility surfaces.
problem Forecasting implied volatility surfaces in foreign exchange markets.
method Dynamic functional principal component analysis and multivariate functional time-series methods.
result Dynamic univariate functional time-series method shows the greatest improvement in forecast accuracy.
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an arbitrary copula is in the domain of attraction of a multivariate extreme value …
New statistical methods improve explainability of boosting models.
problem Uncertainty quantification for boosting models is computationally intensive and hard to interpret.
method Derive methods for statistical inference using gradient boosting and Boulevard regularization.
result Achieve asymptotically normal predictions with theoretical guarantees and runtime independent of data size.
This study compares multivariate vs univariate machine learning for multi-output regression.
problem When to use multivariate ensemble techniques over separate univariate models.
method Comparative analysis of different multivariate approaches for multi-output regression.
result Multivariate ensemble techniques outperform separate univariate models in simulations.
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient gradient computation that enables gradient-based optimization procedures, including…
New formula for efficient spread option pricing in copula markets.
problem Efficient pricing of spread options in markets with correlated assets.
method Unified approach using copula functions and numerical integration.
result Proposes a method requiring only one-dimensional integral evaluations.
This paper improves multi-label ranking by reweighting univariate losses, enhancing consistency and performance.
problem Improving multi-label ranking performance while maintaining consistency.
method Systematic study of consistency and generalization error bounds for learning algorithms, proposing a reweighted univariate loss.
result Inconsistent pairwise losses can lead to better performance than consistent univariate losses in practice.
RAMs improve GAMs' accuracy by fitting components to subregions of feature space.
problem Subpar accuracy in GAMs due to inability to capture feature interactions.
method Identify subregions of feature space where interactions are minimized, fitting one component per subregion.
result RAMs offer improved expressiveness compared to GAMs while maintaining interpretability.
Mirror flow in shallow neural networks shows similar implicit bias to gradient flow, with key differences in curvature penalties.
problem Analyzing implicit bias in shallow neural networks with mirror flow.
method Characterization through variational problems and scaled potentials.
result Mirror flow with scaled potentials induces a rich class of biases not captured by RKHS norms.
Multivariate boosted trees improve forecasting and control by capturing correlated predictions.
problem Capturing multivariate target cross-correlations and applying structured penalties to predictions.
method A computationally efficient algorithm for fitting multivariate boosted trees.
result Multivariate trees outperform univariate counterparts in correlated prediction scenarios.
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate di…
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate O(n−2r/(2r+1)) for Sobolev space functions. This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal ways to construct risk measures are given and extensions to more general situations…
Proposes MVG-CRPS for robust multivariate forecasting.
problem Outliers in multivariate forecasting lead to significant errors.
method Integrates CRPS for MVG distributions, optimizing with MVG-CRPS.
result Improves robustness, accuracy, and uncertainty quantification.
Study assesses drought and late-frost risks in Bavaria using vine copulas.
problem Assessing risks of late-frost and drought in Bavaria due to climate change.
method Used vine copula models for non-Gaussian and asymmetric dependencies, with univariate and bivariate regression analyses.
result Identified 'at-risk' regions for forest adaptation.
DKMD is a fast signed statistic for comparing univariate distributions.
problem Comparing univariate distributions, especially preserving directionality.
method DKMD integrates kernel mean embeddings against an odd weighting function.
result DKMD preserves directionality and is robust to outliers.
A key element of understanding the efficacy of overparameterized neural networks is characterizing how they represent functions as the number of weights in the network approaches infinity. In this paper, we characterize the norm required to realize a function f:Rd→R as a single hidden-lay…
Recent advances in statistical theory, together with advances in the computational power of computers, provide alternative methods to do mass-univariate hypothesis testing in which a large number of univariate tests, can be properly used to compare MEEG data at a large number of time-frequency points and scalp location…
Deep learning methods improve time series forecasting by optimizing lag selection.
problem Optimizing the number of lags for accurate univariate time series forecasting.
method Empirical analysis of deep learning methods trained on multiple time series datasets.
result Excessively small or large lag sizes negatively impact forecasting performance.
In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite L1-norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all po…
Methodology to measure lag relevance in time series models.
problem Measuring lag relevance in machine learning models for univariate time series.
method Ghost variables, Shapley values, additive importance measures, auto-relevance and partial auto-relevance functions, one-step forecast.
result Calculated relevance measures successfully demonstrate expected lag structure in almost all cases.
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, F measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives…
Study learns a projection and function in Gaussian models.
problem Learning a one-dimensional projection and a univariate function in high-dimensional Gaussian models.
method Gradient flow dynamics of alternating scheme, RKHS adaptation.
result Gradient flow dynamics converge with rate controlled by Gaussian regularity.
Hybrid LSTM-fully convolutional networks (LSTM-FCN) for time series classification have produced state-of-the-art classification results on univariate time series. We show that replacing the LSTM with a gated recurrent unit (GRU) to create a GRU-fully convolutional network hybrid model (GRU-FCN) can offer even better p…
Kronecker trend filtering improves lattice data smoothing.
problem Estimating smooth functions on lattice data.
method Penalized least squares with Kronecker products of univariate trend filtering penalties.
result Kronecker trend filtering outperforms linear smoothers in high dimensions.
Time Series forecasting (univariate and multivariate) is a problem of high complexity due the different patterns that have to be detected in the input, ranging from high to low frequencies ones. In this paper we propose a new model for timeseries prediction that utilizes convolutional layers for feature extraction, a r…
We present a novel k-way high-dimensional graphical model called the Generalized Root Model (GRM) that explicitly models dependencies between variable sets of size k > 2---where k = 2 is the standard pairwise graphical model. This model is based on taking the k-th root of the original sufficient statistics of any univa…
Develops a functional mix-of-experts model for multiclass classification.
problem Multiclass classification with univariate functional predictors.
method Functional mix-of-experts model with regularization and sparsity constraints.
result Regularized maximum likelihood estimation yields interpretable coefficient functions.
AdaPTS adapts univariate FMs for multivariate time series forecasting.
problem Challenges in managing feature dependencies and uncertainty quantification in multivariate time series forecasting.
method Adapters that transform multivariate inputs into a latent space and apply univariate FMs independently to each dimension.
result AdaPTS enhances forecasting accuracy and uncertainty quantification compared to baseline methods.
Paper forecasts recession indicators using yield spread models.
problem Forecasting the leading indicator of a recession using yield spread.
method Applied econometric time series and machine learning models to forecast yield spread.
result Parsimonious univariate ARIMA model outperforms richly parameterized VAR method.
Proposes a new method for generating synthetic data using copula flows.
problem Challenges of current synthetic data generation methods, especially with mixed real and categorical variables.
method Uses normalizing flows to learn copula density and univariate marginals based on copula theory.
result Demonstrates improved synthetic data generation and density estimation.
This work introduces a fixed-point optimization for variational inference.
problem Improving quantified uncertainty in predictions by optimizing a simplified distribution over parameters.
method Projective integral updates for high-dimensional variational inference.
result Efficient quasirandom quadrature sequence for mean-field distributions, leading to quasi-Newton variational Bayes (QNVB).
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
Anomalies in time-series data give essential and often actionable information in many applications. In this paper we consider a model-free anomaly detection method for univariate time-series which adapts to non-stationarity in the data stream and provides probabilistic abnormality scores based on the conformal predicti…
Counterexamples show failure of uniform laws of large numbers for subdifferentials.
problem Failure of uniform laws of large numbers for subdifferentials under natural assumptions.
method Univariate and bivariate random Lipschitz and convex functions with smooth pieces.
result Counterexamples demonstrate failure of uniform laws of large numbers for subdifferentials.
We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We present a simulated study regarding the estimation of the risk measure VaRp on FIEGARCH processes. We consider the distr…
We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contribu…
Proposed by Donoho (1997), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article we define and study Dyadic CART and a closely related estimator, namely Optimal Regression Tree (ORT), in the contex…