Related papers: Simulating Raga Notes with a Markov Chain of Order…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
Connectionist sequence models (e.g., RNNs) applied to musical sequences suffer from two known problems: First, they have strictly "absolute pitch perception". Therefore, they fail to generalize over musical concepts which are commonly…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and…
Mamba has recently emerged as a promising alternative to Transformers, offering near-linear complexity in processing sequential data. However, while channels in time series (TS) data have no specific order in general, recent studies have…
Music is a string of some of the notes out of 12 notes (Sa, Komal_re, Re, Komal_ga, Ga, Ma, Kari_ma, Pa, Komal_dha, Dha, Komal_ni, Ni) and their harmonics. Each note corresponds to a particular frequency. When such strings are encoded to…
The analysis of second-order optimization methods based either on sub-sampling, randomization or sketching has two serious shortcomings compared to the conventional Newton method. The first shortcoming is that the analysis of the iterates…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
There are two popular general approaches for the analysis and visualization of a contingency table and a compositional data set: Correspondence analysis (CA) and log ratio analysis (LRA). LRA includes two independently well developed…
Large scale machine learning-based Raga identification continues to be a nontrivial issue in the computational aspects behind Carnatic music. Each raga consists of many unique and intrinsic melodic patterns that can be used to easily…
As generative models have risen in popularity, a domain that has risen alongside is generative models for music. Our study aims to compare the performance of a simple Markov chain model and a recurrent neural network (RNN) model, two…
We study the Order-$k$ ($k \geq 4$) spiked tensor model for the tensor principal component analysis (PCA) problem: given $N$ i.i.d. observations of a $k$-th order tensor generated from the model $\mathbf{T} = \lambda \cdot v_*^{\otimes k} +…
The notes which play the most important and second most important roles in expressing a raga are called Vadi and Samvadi swars respectively in (North) Indian Classical music. Like Bageshree, Bhairavi, Shankara, Hamir and Kalingra, Rageshree…
Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may…
Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this…
Online music databases have increased signicantly as a consequence of the rapid growth of the Internet and digital audio, requiring the development of faster and more efficient tools for music content analysis. Musical genres are widely…
We provide a complete characterization of the randomized Kaczmarz algorithm (RKA) for inconsistent linear systems. The Kaczmarz algorithm, known in some fields as the algebraic reconstruction technique, is a classical method for solving…
We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency…