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.
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
Eigenfunction value distribution shows unimodal density with maximum at zero.
problem Understanding the value distribution of Laplace eigenfunctions.
method Analyzing the measure μ whose density is ∣ablaf∣2 and proving a monotonicity formula. result Eigenfunction value distribution under μ is unimodal with maximum at zero. A new UU-test decides unimodality of datasets.
problem Deciding on the unimodality of a dataset for better data analysis.
method UU-test operates on the empirical cumulative density function (ecdf) to build a piecewise linear approximation that models the data as a Uniform Mixture Model.
result The UU-test provides a statistical model of the data in the form of a Uniform Mixture Model.
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that for a radial log-convex density…
This work improved clustering methods by analyzing various datasets and dendrograms.
problem Avoiding false positives in clustering, especially for unimodal and bimodal data.
method Applied agglomerative clustering methods (single, average, median, complete, centroid, Ward's) to various datasets.
result Many methods detected two clusters in unimodal data, with single-linkage being more resilient.
Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray gene expression data. Many clustering methods are available, but it is challengi…
Proposes models to better represent ordinal data with non-unimodal distributions.
problem Real-world ordinal data often have non-unimodal conditional probability distributions.
method Develops approximately unimodal likelihood models to better represent non-unimodal CPDs.
result Proposed models can effectively represent both unimodal and nearly unimodal CPDs.
GGMPs improve non-Gaussian conditional density estimation.
problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.
method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.
result GGMPs improve distributional approximation on synthetic and real-world datasets.
Hierarchical nucleation patterns emerge in deep neural network layers.
problem Understanding the generation of meaningful representations in deep neural networks.
method Analysis of the probability density of ImageNet dataset across hidden layers.
result Density peaks in subsequent layers mirror the semantic hierarchy of concepts, resembling nucleation process.
Proposes a deep ordinal regression framework using optimal transport loss and unimodal output probabilities.
problem Lack of unimodal output probabilities in recent ordinal regression models.
method Introduces a deep learning framework based on optimal transport loss and unimodal output distribution, inspired by the Proportional Odds model.
result Demonstrates improved performance and unimodal output probabilities on real-world datasets compared to existing methods.
New algorithm optimizes unimodal bandits using empirical divergence.
problem Optimizing decisions in multi-armed bandit problems with unimodal distributions.
method Indexed Minimum Empirical Divergence (IMED) adapted for unimodal structure.
result IMED-UB algorithm optimally exploits unimodal structure.
Proposes new loss functions for better handling bimodal predictive uncertainty.
problem Bimodal predictive uncertainty in machine learning models.
method Family of distribution-aware loss functions integrating normalized RMSE with Wasserstein and Cramér distances.
result Proposed loss functions reduce predictive uncertainty estimation error by 45% on complex bimodal datasets.
Study on unimodality of plucking polynomial with delay function.
problem Exploring unimodality of plucking polynomial with delay function.
method Presented a formula for the plucking polynomial of hedgehog rooted trees and explored unimodality with specific delay functions.
result Found interesting examples and speculations on unimodality of plucking polynomials with delay functions.
This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed un…
This paper strengthens the computational separation between multimodal and unimodal learning, showing unimodal learning is hard on typical instances.
problem Theoretical justification for empirical success of multimodal machine learning.
method Introduced a stronger average-case computational separation between unimodal and multimodal learning.
result For typical instances, unimodal learning is computationally hard, while multimodal learning is easy.
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.
Unimodal sequences of moves connect 3-manifold triangulations.
problem Understanding the structure of sequences of bistellar flips.
method Examined unimodal sequences of moves that increase and decrease triangulation size.
result Proved that any two one-vertex triangulations are connected by a unimodal sequence of moves.
We classify rooted trees which have strictly unimodal q-polynomials (plucking polynomial). We also give criteria for a trapezoidal shape of a plucking polynomial. We generalize results of Pak and Panova on strict unimodality of q-binomial coefficients. We discuss which polynomials can be realized as plucking polynomial…
Despite the advances in the representational capacity of approximate distributions for variational inference, the optimization process can still limit the density that is ultimately learned. We demonstrate the drawbacks of biasing the true posterior to be unimodal, and introduce Annealed Variational Objectives (AVO) in…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function is known, mode is an argument of the maximum value of the density function and o…
New strategies avoid forced exploration for unimodal bandits.
problem Optimal exploration of unimodal bandit problems.
method Adapting IMED strategy to unimodal structure without forced exploration.
result Proven optimal strategies for unimodal bandits.
High-dimensional unimodal distributions can cause MCMC methods to fail.
problem Failure of MCMC methods in high-dimensional unimodal distributions.
method Examples and theoretical analysis of MCMC methods, including Metropolis-Hastings adjusted methods.
result MCMC methods can take an exponential run-time for high-dimensional unimodal distributions.
New method improves on existing algorithms for rank-one bandits.
problem Minimizing regret in stochastic rank-one bandits.
method Unimodal Thompson Sampling (UTS) with new analysis.
result UTS provides an asymptotically optimal regret bound.
We consider stochastic multi-armed bandits where the expected reward is a unimodal function over partially ordered arms. This important class of problems has been recently investigated in (Cope 2009, Yu 2011). The set of arms is either discrete, in which case arms correspond to the vertices of a finite graph whose stru…
Paper introduces kernel deformed exponential families for sparse continuous attention.
problem Creating efficient attention mechanisms for sparse data.
method Developed kernel deformed exponential families, theoretically and experimentally.
result Kernel deformed exponential families can attend to multiple compact regions of data.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Study calculates slope gaps on polygon surfaces, finding non-unimodal distributions.
problem Understanding the distribution of slope gaps on polygon surfaces.
method Explicit computation of slope gap distributions for 2n-gons, providing bounds on non-differentiability points.
result Slope gap distributions are not always unimodal, answering a question by Athreya.
Proposes methods for local clustering in attributed graphs.
problem Finding a single cluster concentrated on a specific region in a graph.
method Introduces Graph Unimodality (GU) and Attribute Unimodality (AU) measures, and LOCLU algorithm to optimize Compactness score.
result Local cluster detected by LOCLU concentrates on the region of interest and exhibits unimodal data distribution.
We present an efficient approach for leveraging the knowledge from multiple modalities in training unimodal 3D convolutional neural networks (3D-CNNs) for the task of dynamic hand gesture recognition. Instead of explicitly combining multimodal information, which is commonplace in many state-of-the-art methods, we propo…
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate …
Study on financial systems using perturbed unimodal maps with heteroscedastic noise.
problem Analyzing systemic risk in financial systems using mathematical models.
method Investigation of one-dimensional unimodal maps perturbed by heteroscedastic noise, proving stability, convergence, and Lyapunov exponent continuity.
result Continuous dependence of average Lyapunov exponent on Markov chain parameters, and Gumbel's law for extreme values.
TCT learns multimodal sequence representations by translating from related sequences.
problem Challenges in learning semantic representations from multimodalities.
method Transformer based Cross-modal Translator (TCT) combined with Multimodal Transformer Network (MTN).
result Proposed method achieves new state-of-the-art performance on video-grounded dialogue.
Paper tackles imbalanced time series classification with a novel oversampling method.
problem Imbalanced time series classification challenges due to high dimensionality and correlation.
method Density-ratio based clustering followed by shrinkage technique for covariance estimation, then generating synthetic samples.
result OHIT outperforms state-of-the-art methods in F1, G-mean, and AUC metrics.
New algorithm reduces regret in multi-armed bandit problems with Gaussian rewards.
problem Optimizing decisions in multi-armed bandit problems with Gaussian rewards.
method Proposed TSCG and UTSCG algorithms using Thompson Sampling with Gaussian prior.
result Achieved lower regret bounds for optimal arm selection.
An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by the invariant foliations is described, and is shown to make S into a complex sp…
TA-CQR predicts regression intervals with exact coverage, splitting miscoverage between endpoints.
problem Predicting regression intervals with exact coverage under reporting constraints.
method TA-CQR uses tail allocation to parameterize the oracle, estimating the allocation by searching quantile cores and applying nonnegative additive split-conformal calibration.
result TA-CQR achieves exact finite-sample marginal coverage under exchangeability, with theoretical guarantees on calibration and length.
GONs improve predictions of maximizers from noisy black-box functions.
problem Estimating maximizers of noisy black-box functions.
method Global Optimization Networks (GONs) composed of invertible and unimodal functions.
result GONs outperform convex fits, GPR, and DNNs in prediction accuracy.
Simple baselines improve multimodal utterance learning.
problem Learning rich multimodal utterance representations.
method Conditional factorization of utterances into unimodal factors; extending to bimodal and trimodal factors.
result Optimal embeddings can be derived in closed form.
Paper presents a unified approach to interpolation and geodesics in latent spaces of generative models.
problem Finding geodesics and interpolating in latent spaces of non-Gaussian densities.
method General approach to interpolation and geodesics in latent space for arbitrary density.
result Maximizing quality measure of an interpolating curve is equivalent to finding geodesic.
Paper introduces clock moves for plane graphs and proves Alexander polynomial properties.
problem Alexander polynomial of plane graphs and unimodality of coefficients.
method Introduces clock moves for plane graphs and develops a spanning tree model of Alexander polynomial.
result Proves unimodal property of Alexander polynomial coefficients and confirms conjectures.
Unimodal approach for group-level emotion recognition without individual features.
problem Privacy issues in individual-based emotion recognition models.
method Frugal approach using global features, state-of-the-art and synthetic corpora.
result 59.13% accuracy on VGAF test set, 11th place in EmotiW Challenge 2020.
Paper proposes a method to preserve multimodal sentiment analysis fidelity.
problem Lack of fidelity in multimodal fusion for sentiment analysis.
method Variational autoencoder-based approach for modality fusion.
result Empirically shows superior performance over state-of-the-art methods.
We find stationary distributions in a financial model with trends and mean-reversion.
problem Financial markets with competing trends and mean-reversion.
method Analytical derivation of stationary distributions in various noise and feedback regimes.
result The distributions are unimodal Gaussians in small noise, small feedback limits, but can be bimodal for stronger trends.
RAHMC improves sampling from multimodal distributions using dissipative dynamics.
problem Sampling from multimodal distributions efficiently.
method RAHMC uses mode-repelling and mode-attracting stages with a single tuning parameter.
result RAHMC generates proposals that cross low-probability barriers efficiently.
We propose a differentiable sigmoid function for efficient p-value calculation in clustering.
problem Efficient and accurate p-value calculation for clustering algorithms.
method Designed a differentiable sigmoid function to approximate the Dip-p-value transformation.
result Accelerates computation and integrates well with gradient descent-based learning schemes.
We solve a century-old conjecture about Alexander polynomials of special alternating links.
problem Fox's conjecture about unimodality of Alexander polynomial coefficients.
method Proving a multivariate generalization of the Alexander polynomial is Lorentzian.
result Alexander polynomial coefficients of special alternating links form a log-concave sequence.
Algorithm bounds causal queries under selection bias.
problem Selection bias affects causal analysis.
method Proposes a new algorithm to address both identifiable and unidentifiable causal queries.
result The likelihood of available data is unimodal, enabling bounds on causal queries.