A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers approximate partition functions on Riemannian spaces in the large N limit.
New algorithm extends Greville's method for partitioned matrices efficiently and stably.
New method connects neural networks to diagrammatic algebra.
This paper tackles fitting multilevel low rank matrices by addressing three problems.
In this paper, we provide an approach to clustering relational matrices whose entries correspond to either similarities or dissimilarities between objects. Our approach is based on the value of information, a parameterized, information-theoretic criterion that measures the change in costs associated with changes in inf…
Origin-destination (OD) matrices are often used in urban planning, where a city is partitioned into regions and an element (i, j) in an OD matrix records the cost (e.g., travel time, fuel consumption, or travel speed) from region i to region j. In this paper, we partition a day into multiple intervals, e.g., 96 15-min …
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.
ALMA improves clustering of multilayer networks.
Graph energy helps detect communities in networks better than traditional methods.
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and pro…
The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some prev…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each partition set. We propose an alternative approach, which avoids such partitioning and…
Improved spectral clustering via Gromov-Wasserstein Learning.
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.
The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. Firs…
We present two simple ways of reducing the number of parameters and accelerating the training of large Long Short-Term Memory (LSTM) networks: the first one is "matrix factorization by design" of LSTM matrix into the product of two smaller matrices, and the second one is partitioning of LSTM matrix, its inputs and stat…
The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with straight edges from the determinant of a matrix of size 2N, where N denotes the number of edges of G. In this paper, we extend this formula to any finite graph: the partition function can be written as an alternating sum of the…
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in sma…
Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matri…
This paper proposes a stochastic model using the concept of Markov chains for the inter-state transitions of the millisecond order quasi-stable phase synchronized patterns or synchrostates, found in multi-channel Electroencephalogram (EEG) signals. First and second order transition probability matrices are estimated fo…
The paper improves clustering algorithms for noisy data samples.
A method for community detection in multilayer networks using data matrices.
In this report, we present an unsupervised machine learning method for determining groups of molecular systems according to similarity in their dynamics or structures using Ward's minimum variance objective function. We first apply the minimum variance clustering to a set of simulated tripeptides using the information …
A new method clusters data from multiple sources using a mixture of multilayer SBMs.
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing size, complexity and dimensionality of the problems. In particular, covariance mat…
New neural networks for non-commutative data.
Computing the permanent of a non-negative matrix is a core problem with practical applications ranging from target tracking to statistical thermodynamics. However, this problem is also #P-complete, which leaves little hope for finding an exact solution that can be computed efficiently. While the problem admits a fully …
Decision Machines embeds decision trees into vector spaces for improved optimization.
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. As a case study, a state-of-the-art neural language model usually consists of one or more recurrent layers sandwiched between an embedding layer used for representing inp…
Kernel methods summarize and integrate posterior similarity matrices from Bayesian clustering.
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…
The meridian maps of the full Homfly skein of the annulus are linear endomorphisms induced by the insertion of a meridian loop, with either orientation, around a diagram in the annulus. The eigenvalues of the meridian maps are known to be distinct, and are indexed by pairs of partitions of integers p and n into k and k…
Lomonaco and Kauffman introduced knot mosaic system to give a definition of quantum knot system. This definition is intended to represent an actual physical quantum system. A knot -mosaic is an matrix of mosaic tiles which are through depicted as below, representing a knot or a link b…
The study limits how many parts regular simplicial partitions can overlap.
Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.
A method for identifying joint and individual subspaces from multi-view data.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …
New method speeds up Gaussian process training and inference for large datasets.
New method for summarizing Bayesian mixture models using sliced Wasserstein distances.
Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the 2-year period 1994-95 and (ii) 1-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find that the eigenvectors o…
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing group-level differences, i.e., in identifying if trends of estimated ob…
In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…
The study examines the balancedness of random partition models and finds the rich-get-richer characteristic is a result of model assumptions.
The paper develops mixed-integer formulations for neural networks using partitioning.
New partition designs reduce star discrepancy in high-dimensional sampling.
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including variants of multi-level methods and spectral clustering. We propose GAP, a Generaliz…