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.
Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …
Improves matrix multiplication throughput for asymmetric bit-width operands.
problem Matrix multiplications between asymmetric bit-width operands, especially 8- and 4-bit, are not efficiently handled by existing SIMD instructions.
method Proposes a new SIMD matrix multiplication instruction that uses mixed precision on inputs (8- and 4-bit) and accumulates into 16-bit output, improving throughput.
result Offers 2x improvement in throughput compared to existing symmetric-operand-size instructions, with negligible overflow.
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of Bernstein's inequality and a tail inequality for quadratic forms in subgaussian random ve…
Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the individuality and commonality of multi-view data can be leveraged to generate high-quality …
DMClusts discovers multiple clusterings from multi-view data.
problem Finding multiple meaningful and diverse clusterings from multi-view data.
method Deep matrix factorization to gradually factorize multi-view data into representational subspaces and generate one clustering per layer, enforcing diversity through proximity minimization.
result DMClusts outperforms state-of-the-art multiple clustering solutions.
Transfer knowledge from multiple sources to improve matrix completion.
problem Matrix completion with noisy data.
method Aggregating singular subspaces information from multiple sources to solve a two-way PCA problem and transform into a low-dimensional linear regression.
result Guaranteed statistical efficiency in transforming the high-dimensional target matrix completion problem.
We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in …
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual serie…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources whic…
The matrix-based Renyi's α-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's α-order entropy functional only defines the entropy of a single…
Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched versio…
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the flexibility of the model by parameterizing the model matrix. By imposing restrictions …
Linear algebra algorithms are used widely in a variety of domains, e.g machine learning, numerical physics and video games graphics. For all these applications, loop-level parallelism is required to achieve high performance. However, finding the optimal way to schedule the workload between threads is a non-trivial prob…
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multi…
This paper identifies and estimates the label noise transition matrix without ground truth labels.
problem Learning with noisy labels and identifying the noise transition matrix.
method Building on Kruskal's identifiability results, the paper characterizes the identifiability of the label noise transition matrix for the generic case at the instance level.
result The necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level.
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…
Advances in molecular "omics'" technologies have motivated new methodology for the integration of multiple sources of high-content biomedical data. However, most statistical methods for integrating multiple data matrices only consider data shared vertically (one cohort on multiple platforms) or horizontally (different …
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic nonnegative matrix factorization (NMF) to extract short-lived temporal motifs from a long …
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most popular, but which h…