Related papers: Hidden Markov Models with Momentum
Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…
LLM-based prompt optimization, that uses LLM-provided "textual gradients" (feedback) to refine prompts, has emerged an effective method for automatic prompt engineering. However, its scalability and stability are unclear when using more…
Model stealing, where a learner tries to recover an unknown model via carefully chosen queries, is a critical problem in machine learning, as it threatens the security of proprietary models and the privacy of data they are trained on. In…
Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov's acceleration techniques to match…
An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational…
The adaptive stochastic gradient descent (SGD) with momentum has been widely adopted in deep learning as well as convex optimization. In practice, the last iterate is commonly used as the final solution to make decisions. However, the…
The success of large language models has garnered widespread attention for model merging techniques, especially training-free methods which combine model capabilities within the parameter space. However, two challenges remain: (1) uniform…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
We analyze gradient descent with Polyak heavy-ball momentum (HB) whose fixed momentum parameter $\beta \in (0, 1)$ provides exponential decay of memory. Building on Kovachki and Stuart (2021), we prove that on an exponentially attractive…
Distributed stochastic gradient methods are widely used to preserve data privacy and ensure scalability in large-scale learning tasks. While existing theory on distributed momentum Stochastic Gradient Descent (mSGD) mainly focuses on…
Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This…
The Expectation Maximization (EM) algorithm is a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be…
Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past…
We show how models for prediction with expert advice can be defined concisely and clearly using hidden Markov models (HMMs); standard HMM algorithms can then be used to efficiently calculate, among other things, how the expert predictions…
In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the…
Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…
Hidden Markov model (HMM) has been successfully used for sequential data modeling problems. In this work, we propose to power the modeling capacity of HMM by bringing in neural network based generative models. The proposed model is termed…
We propose a new method for the estimation of parameters of hidden diffusion processes. Based on parametrization of the transition matrix, the Baum-Welch algorithm is improved. The algorithm is compared to the particle filter in application…
The hidden Markov model (HMM) is a widely-used generative model that copes with sequential data, assuming that each observation is conditioned on the state of a hidden Markov chain. In this paper, we derive a novel algorithm to cluster HMMs…
A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…