arXiv research

Paper improves feature selection accuracy using transfer learning.

Cross-validation estimates model performance on unseen data, not training data.

The Mallows model, introduced in the seminal paper of Mallows 1957, is one of the most fundamental ranking distribution over the symmetric group $S_m$. To analyze more complex ranking data, several studies considered the Generalized Mallows model defined by Fligner and Verducci 1986. Despite the significant research in…

Paper extends top-k Mallows model for better user preference analysis.

The paper tackles learning true rankings from noisy, incomplete data.

The paper proposes methods to identify and sample from mixtures of Mallows models for top-k rankings.

We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our k…

Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we give the first polynomial time algorithm for provably learning the parameters of…

Extends Mallows model to handle item indifference in rankings.

New algorithm learns permutations mixtures with optimal sample complexity.

The paper addresses model averaging and ensembling, providing theoretical and practical insights.

Paper proposes a new anomaly detection method using Random Forest with Mallows-like criterion.

New voting rules protect against strategic voting by robust statistics.

We generalize Mallows model to learn distance metrics from data.

Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems …

Unified model combines scores and rankings for grant panel review.

This paper protects rankings from differential privacy breaches.

We analyze the generalized Mallows model, a popular exponential model over rankings. Estimating the central (or consensus) ranking from data is NP-hard. We obtain the following new results: (1) We show that search methods can estimate both the central ranking pi0 and the model parameters theta exactly. The search is n!…

The study of isospectral surfaces in Euclidean and hyperbolic geometries.

We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…

We prove that the connected sums CP_2 # CP_2 and CP_2 # CP_2 # CP_2 admit self-dual metrics with positive Ricci curvature. Moreover, every self-dual metric of positive scalar curvature on CP_2 # CP_2 is conformal to a metric with positive Ricci curvature.

Extends Fisher's Discriminant Analysis for interval-valued data.

The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it has captured the attention of the optimization community for decades. As a resu…

Here we draw a handlebody picture for the exotic CP^2 # 2(-CP^2) constructed by Akhmedov and Park.

Here we draw a handlebody picture for the exotic CP^2 # 3(-CP^2), constructed by Akhmedov and Park.

This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Sh…

A new algorithm speeds up CP decomposition for large tensors.

The paper explores the genus of surfaces in complex projective spaces and improves minimal genus bounds.

In this paper we construct a minimal symplectic 4-manifold and prove it is homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)

Motivated by a construction of Fintushel and Stern, we show that the topological 4--manifold $CP^2#5{\bar CP^2}$ supports infinitely many distinct smooth structures.

The paper applies communication theory to improve language model reranking.

In this short note we show that the existence of bilaterally symmetric extremal Kähler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$.

The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are $\mathbb{CP}^1$ and $\mathbb{CP}^2$ is used.

In 1983, Banchoff and Kuhnel constructed a minimal triangulation of $\CP^2$ with 9 vertices. $\CP^3$ was first triangulated by Bagchi and Datta in 2012 with 18 vertices. Known lower bound on number of vertices of a triangulation of $\CP^n$ is $1 + \frac{(n + 1)^2}{2}$ for $n \geq 3$. We give explicit construction of so…

Hierarchical Partial-Order Models for Ranking

Page's Einstein metric on CP_2 # (-CP_2) is conformally related to an extremal Kaehler metric. Here we construct a family of conformally Kähler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kaehler cone of CP_2 # (-CP_2).The same method also yields analogous sol…

Study on slicing knots in 4-manifolds, focusing on CP^2-slicing numbers.

We construct potentially new manifolds homeomorphic but not diffeomorphic to $\mathbb{CP}^{2} \# 8 \overline{\mathbb{CP}^{2}}$ and $\mathbb{CP}^{2} \# 9 \overline{\mathbb{CP}^{2}}$ via rational blowdown surgery along certain $4$-valent plumbing graphs. This way all the graph classes from \cite{weighted} have a represen…

In this paper we describe how to define the circle packing (cp) type(either cp parabolic or cp hyperbolic) of a Riemann surface of class $\mathcal{S}$, and study the relation between this type and the conformal type of the surface.

We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP^2 # p (-CP^2) for p=7, 8, 9, and to 3 CP^2 #q (-CP^2) for q =12,...,19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spa…

Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to $M$. We also construct such exotic smooth structure…

Novel algorithm optimizes decision trees for nonlinear metrics.

As an application of `reverse engineering' technique introduced by R. Fintushel, D. Park and R. Stern \cite{FPS}, we construct an infinite family of fake (2n+2l-1)CP^2#(2n+4l-1)(-CP^2)'s for all n \ge 0, l \ge 1.

For 5 <= k <= 8 we show that the infinite family of exotic smooth structures on CP^2# k(-CP^2) can be achieved by 1/n - surgeries on a single embedded nullhomologous torus in a manifold R_k which is homeomorphic to CP^2# k(-CP^2).

We use Hamiltonian actions to construct nonstandard (as opposed to $\RP^n$ and $T^n$) Lagrangian submanifolds of $\CP^n$. First of all, a quotient of $\RP^3$ by the dihedral group $D_3$ is a Lagrangian submanifold of $\CP^3$. Secondly, $\Su(n)/\Z_n$ are Lagrangian submanifolds of $\CP^{n^2-1}$.

We show that the manifold *CP^2 # *RP^4, which is homotopy equivalent but not homeomorphic to CP^2 # RP^4, is in fact smoothable.

A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-towers up to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely d…

We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants in terms of Mock modular forms.