arXiv research

Unimodal sequences of moves connect 3-manifold triangulations.

Multimodalities provide promising performance than unimodality in most tasks. However, learning the semantic of the representations from multimodalities efficiently is extremely challenging. To tackle this, we propose the Transformer based Cross-modal Translator (TCT) to learn unimodal sequence representations by trans…

Paper introduces clock moves for plane graphs and proves Alexander polynomial properties.

We solve a century-old conjecture about Alexander polynomials of special alternating links.

Log-concave coefficient sequences for two-bridge knots proved.

Proposes models to better represent ordinal data with non-unimodal distributions.

A new UU-test decides unimodality of datasets.

Proposes a method to partition univariate data into unimodal subsets.

Proposes a deep ordinal regression framework using optimal transport loss and unimodal output probabilities.

New algorithm optimizes unimodal bandits using empirical divergence.

Study on unimodality of plucking polynomial with delay function.

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 studies the Riley polynomial of 2-bridge knots using Chebyshev polynomials.

Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.

This paper strengthens the computational separation between multimodal and unimodal learning, showing unimodal learning is hard on typical instances.

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…

New strategies avoid forced exploration for unimodal bandits.

High-dimensional unimodal distributions can cause MCMC methods to fail.

Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new families of $q$-hypergeometric series generalizing the Kontsevich-Zagier series. Comparing with the cyc…

Magnetic resonance imaging (MRI) is being increasingly utilized to assess, diagnose, and plan treatment for a variety of diseases. The ability to visualize tissue in varied contrasts in the form of MR pulse sequences in a single scan provides valuable insights to physicians, as well as enabling automated systems perfor…

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…

For a Catalan state $C$ of a lattice crossing $L\left( m,n\right)$ with no returns on one side, we find its coefficient $C\left( A\right)$ in the Relative Kauffman Bracket Skein Module expansion of $L\left( m,n\right)$. We show, in particular, that $C\left( A\right)$ can be found using the plucking polynomial of a …

The paper calculates bounds for risk metrics and entropies under partial information constraints.

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…

Study calculates slope gaps on polygon surfaces, finding non-unimodal distributions.

Proposes methods for local clustering in attributed graphs.

The paper tackles online learning problems with monotone arm sequences, achieving optimal or near-optimal regret bounds.

The Links-Gould invariant of alternating links has log-concave coefficients.

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…

Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank…

SocialInteractionGAN generates realistic human interactions from low-dimensional data.

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 …

The paper proves infinitely many strong symplectic fillings for cusp singularity links.

Study on financial systems using perturbed unimodal maps with heteroscedastic noise.

New algorithm reduces regret in multi-armed bandit problems with Gaussian rewards.

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…

Human language is a rich multimodal signal consisting of spoken words, facial expressions, body gestures, and vocal intonations. Learning representations for these spoken utterances is a complex research problem due to the presence of multiple heterogeneous sources of information. Recent advances in multimodal learning…

GONs improve predictions of maximizers from noisy black-box functions.

The paper studies how arm selection in a bandit problem changes with shape constraints.

Multimodal fusion is considered a key step in multimodal tasks such as sentiment analysis, emotion detection, question answering, and others. Most of the recent work on multimodal fusion does not guarantee the fidelity of the multimodal representation with respect to the unimodal representations. In this paper, we prop…

This work improved clustering methods by analyzing various datasets and dendrograms.

Unimodal approach for group-level emotion recognition without individual features.

We find stationary distributions in a financial model with trends and mean-reversion.

We propose a differentiable sigmoid function for efficient p-value calculation in clustering.

Algorithm bounds causal queries under selection bias.

This work uses ANOVA to understand how different factors contribute to test error in machine learning models.

Unified model integrates text and time series for financial forecasting.

We introduce Disease Knowledge Transfer (DKT), a novel technique for transferring biomarker information between related neurodegenerative diseases. DKT infers robust multimodal biomarker trajectories in rare neurodegenerative diseases even when only limited, unimodal data is available, by transferring information from …