Paper proposes a shape-constrained approach to distributionally robust learning.
problem Challenges in statistical learning under distribution shift.
method Shape-constrained approach to distributionally robust learning (DRL). Assumes isotonic density ratio.
result Improved accuracy demonstrated in empirical studies.
New algorithms reduce rejection sampling complexity for shape-constrained distributions.
problem Generating exact samples from shape-constrained distributions efficiently.
method Sublinear query complexity algorithms for rejection sampling.
result Sublinear complexity algorithms for sampling from shape-constrained distributions.
Shape-constrained symbolic regression improves model extrapolation with prior knowledge.
problem Improving model extrapolation with prior knowledge in symbolic regression.
method Shape-constrained symbolic regression using evolutionary algorithms with interval arithmetic.
result Models with shape constraints have improved extrapolation but lower accuracy on test sets.
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
HyCNNs improve convex function learning and optimal transport.
problem Learning and optimizing convex functions efficiently.
method Combining Maxout networks and ICNNs to create a new neural architecture.
result HyCNNs require fewer parameters and outperform existing methods in convex tasks.
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function f from independent pairs (xi,yi) where E[yi]=f(xi),i=1,…n. While this problem is well understood both statistically and computationally, much l…
We consider N-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank appr…
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied to any pre-trained prediction rule, while the second method deals specifically w…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a modified version of the usual likelihood ratio statistic, that we call "the split li…
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating such value functions plays an important role in approximate dynamic programming and applied probability in general. We incorporate "soft in…
Proposes a tuning-free dynamic pricing method for linear valuation models.
problem Dynamic pricing in linear valuation models with unknown market noise distribution.
method Shape-constrained isotonic regression under weaker Hölder continuity assumptions.
result Demonstrates lower empirical regret compared to existing methods.
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimatio…
Study minimax risk of score estimation for log-concave distributions.
problem Minimizing risk in score estimation for log-concave distributions.
method Developed subclasses of log-concave densities and constructed a locally adaptive, multiscale estimator.
result Established minimax rates for score estimation over specific subclasses of log-concave densities.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
ICCNLS models complex relationships as convex and concave components.
problem Complex input-output relationships with affine ambiguity.
method Sub-gradient constrained affine functions, global orthogonality constraints, L1, L2, and elastic net regularisation.
result Improved predictive accuracy and model simplicity compared to conventional methods.
Paper tackles hard shape constraints in kernel machines.
problem Enforcing shape requirements in a hard fashion is challenging.
method Tightened second-order cone constrained reformulation for kernel machines.
result Performance guarantees and efficiency demonstrated in various applications.
New algorithms solve large-scale convex regression problems.
problem Large-scale convex regression with subgradient regularization.
method Active set type algorithm on dual QP, approximate optimization, randomized augmentation.
result Solves problems with n=10^5 and d=10 in minutes.
A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.
problem Optimizing decisions in sequential problems with context-dependent rewards.
method Proposes a UCB algorithm using a shape-constrained reward function estimator based on a Gaussian Process model with concavity constraints.
result Derives regret bounds for the proposed UCB algorithm.
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
Estimates self- and cross-impact concavity and decay patterns in financial markets.
problem Understanding the impact of financial transactions on market dynamics.
method Nonparametric estimation of concave multi-asset propagator models using metaorders and order flow data.
result Concave self-impact with shifted power-law decay, significant gain from cross-impact, and improved predictive accuracy.
Dynamic pricing policy converges to Nash equilibrium with low regret.
problem Sequential price competition among sellers over multiple periods.
method Semi-parametric least-squares estimation of s-concave demand functions.
result Prices converge to Nash equilibrium with rate O(T−1/7) and sellers incur regret O(T5/7). Venn diagrams are a graphical way to represent a set system. Each of the n sets is represented by a simple closed curve. The n curves subdivide the plane into 2^n open connected regions, each of which represents the intersection of its containing curves' sets. For example, two overlapping circles can divide the plane i…
ecpc R-package improves high-dimensional prediction with co-data.
problem High-dimensional prediction with more variables than samples.
method Adaptive ridge penalised models with co-data, including continuous co-data.
result Improved variable selection and prediction performance.
The paper proposes a method to align AI models using conformal risk control.
problem Aligning AI models to meet end-user requirements in non-generative settings.
method Post-processing a pre-trained model to better align with a subset of functions using conformal risk control.
result A probabilistic guarantee that the resulting conformal interval around a model contains a function approximately satisfying a desired property.
The paper explores solutions to the distributional Bellman equation in reinforcement learning.
problem Distributional reinforcement learning considers complete return distributions, not just expected returns.
method Study existence and uniqueness of solutions to general distributional Bellman equations, linking them to multivariate affine equations.
result Any solution to a distributional Bellman equation can be derived from a multivariate affine distributional equation.
Proposes vMF distribution for skewed elliptical distributions.
problem Skewed distributions not adequately modeled by symmetric distributions.
method Introduces von-Mises-Fisher (vMF) distribution to represent skewed elliptical distributions.
result vMF distribution provides an explicit and simple probability representation of skewed elliptical distributions.
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive…
Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and that of the data distribution, a problem found in widely used deep generative mo…
Method uses optimal transport to complete distributional matrices.
problem Matrix completion for distributional data.
method Nearest neighbors in Wasserstein space.
result Method recovers distributions in Wasserstein metric.
Income and wealth distribution affect stability of a society to a large extent and high inequality affects it negatively. Moreover, in the case of developed countries, recently has been proven that inequality is closely related to all negative phenomena affecting society. So far, Econophysics papers tried to analyse in…
Study clusters distributions with known or unknown clusters using distribution testing.
problem Cluster distributions that are ε-far in total variation. method Distribution testing approach to establish upper and lower bounds on sample complexity.
result Achieves tight sample complexity bounds for all regimes (up to a logarithmic factor).
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these di…
A new distribution family extends the α-stable distribution with a degree of freedom parameter.
problem Lack of moments in the α-stable distribution. method Wright function framework to combine and extend distribution families.
result Generalized α-stable distribution with valid moments. Paper develops a new method to improve model calibration under distribution shifts.
problem Challenges in uncertainty quantification with different training and test distributions.
method Develops multi-domain temperature scaling to handle distribution shifts.
result Outperforms existing methods on in-distribution and out-of-distribution test sets.
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
Researchers derived formulas for joint moments of elliptical distributions.
problem Calculating joint moments of elliptical distributions.
method Used Stein's lemma and two different methods to derive expressions.
result New formulae for expectations of product of normally distributed random variables and simplified expressions for other distributions.
Paper proposes a new method for designing materials using deep learning.
problem Designing high-performance material distributions from given distributions.
method Iterative process of selecting, generating, and merging material distributions using a deep generative model.
result The method improves material performance through iterative refinement.
One-shot algorithm for feature-distributed kernel PCA reduces communication costs.
problem Efficiently perform kernel PCA in distributed computing environments.
method Inspired by dual relationship between sample-distributed and feature-distributed scenarios, proposes a one-shot algorithm for feature-distributed kernel PCA.
result The algorithm provides high-quality results with low communication costs, especially when eigenvalues decay fast.
Paper finds how many neurons are needed to approximate histogram distributions.
problem How many neurons are needed to approximate a target probability distribution?
method Examined for uniform input distribution and histogram target distributions, using efficient neural net construction.
result Obtained a new upper bound on the number of required neurons, strictly better than previous bounds.
Paper analyzes origami slope gaps and their distribution, finding a unique pattern.
problem Analyzing slope gaps in origami surfaces.
method Derived slope gap distribution of a specific origami by considering return times under the horocycle flow.
result Found a unique distribution of origami slope gaps, not a sum of scaled Hall distributions.
A new distributed clustering framework using distributional kernel.
problem Clustering in distributed networks with arbitrary shapes, sizes, and densities.
method Distributed Clustering based on Distributional Kernel (KDC) using similarity of distributions.
result KDC guarantees equivalent clustering outcomes to centralized methods, reduces runtime, and discovers arbitrary clusters.
Paper introduces a new distributional successor measure for reinforcement learning.
problem Learning the distributional consequences of behavior in reinforcement learning.
method Formulates distributional successor measure as a distribution over distributions, proposes algorithm to learn it from data.
result Demonstrates zero-shot risk-sensitive policy evaluation.
The paper extends distributions by singular curves, revealing structural equivalences.
problem Extending (3,6)-distributions using singular curves. method Using data from singular curves, the paper extends (3,6)-distributions to higher rank distributions. result The equivalence of classification problems for four extended distribution classes.
Random matrix ensembles yield uniform distributions on manifolds.
problem Understanding distributions of vectors in random matrix ensembles.
method Analyzing eigenvalues, singular values, and Autonne-Takagi vectors of various random matrix ensembles.
result Uniform distributions on specific manifolds for different types of random matrix ensembles.
New distributions allow greedy arm selection in sparse bandit problems.
problem Sparse contextual bandit problem with sparse parameters and feature distributions.
method Introduced new distribution classes and demonstrated that mixtures of these distributions are also greedy-applicable.
result Greedy algorithm applicable to a wider range of arm feature distributions, including those with origin-asymmetric support.