Related papers: Learning Overcomplete HMMs
The rapid adaptation ability of auto-regressive foundation models is often attributed to the diversity of their pre-training data. This is because, from a Bayesian standpoint, minimizing prediction error in such settings requires…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
Existing unsupervised hash learning is a kind of attribute-centered calculation. It may not accurately preserve the similarity between data. This leads to low down the performance of hash function learning. In this paper, a hash algorithm…
We propose DenseHMM - a modification of Hidden Markov Models (HMMs) that allows to learn dense representations of both the hidden states and the observables. Compared to the standard HMM, transition probabilities are not atomic but composed…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
In this work, we observe that many existing self-supervised learning algorithms can be both unified and generalized when seen through the lens of equivariant representations. Specifically, we introduce a general framework we call…
Through extensive experience developing and explaining machine learning (ML) applications for real-world domains, we have learned that ML models are only as interpretable as their features. Even simple, highly interpretable model types such…
Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…
Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…
Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue,…
This paper studies the sample-efficiency of learning in Partially Observable Markov Decision Processes (POMDPs), a challenging problem in reinforcement learning that is known to be exponentially hard in the worst-case. Motivated by…
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…
We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural…
The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly…
MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive…
Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to…
Overfitting describes a machine learning phenomenon where the model fits too closely to the training data, resulting in poor generalization. While this occurrence is thoroughly documented for many forms of supervised learning, it is not…
In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…