Related papers: Hidden Markov Models with Momentum
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
We introduce $\mathbf{G}$radient Descent with $\mathbf{A}$daptive $\mathbf{M}$omentum $\mathbf{S}$caling ($\mathbf{Grams}$), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning.…
Composition optimization is widely-applied in nonconvex machine learning. Various advanced stochastic algorithms that adopt momentum and variance reduction techniques have been developed for composition optimization. However, these…
Overshoot is a novel, momentum-based stochastic gradient descent optimization method designed to enhance performance beyond standard and Nesterov's momentum. In conventional momentum methods, gradients from previous steps are aggregated…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Recent progress on deep learning relies heavily on the quality and efficiency of training algorithms. In this paper, we develop a fast training method motivated by the nonlinear Conjugate Gradient (CG) framework. We propose the Conjugate…
Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient $\beta$. Large $\beta$ values can potentially…
As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…
We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models. While ML estimator works by (locally) maximizing the…
The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability assigned to element $\gamma$ is multiplied by $(1 -\epsilon…
Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the…
Since Polyak's pioneering work, heavy ball (HB) momentum has been widely studied in minimization. However, its role in min-max games remains largely unexplored. As a key component of practical min-max algorithms like Adam, this gap limits…
The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning…
Training a modern machine learning architecture on a new task requires extensive learning-rate tuning, which comes at a high computational cost. Here we develop new Polyak-type adaptive learning rates that can be used on top of any momentum…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
Autonomous agents require the capability to identify dynamic objects in their environment for safe planning and navigation. Incomplete and erroneous dynamic detections jeopardize the agent's ability to accomplish its task. Dynamic detection…
Behavior trees are rapidly attracting interest in robotics and human task-related motion tracking. However no algorithms currently exist to track or identify parameters of BTs under noisy observations. We report a new relationship between…
The stochastic gradient descent method with momentum (SGDM) is a common approach for solving large-scale and stochastic optimization problems. Despite its popularity, the convergence behavior of SGDM remains less understood in nonconvex…
Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a…
In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…