Usingcollectedindirect measurements and the forward model, the goal becomes to recover the source. When the forward model is unknown, or imperfect, artifacts due to model mismatch occur in the recovery of the source.

Learning the parameters of Partially Observable Markov Decision Processes (POMDPs) from limited data is a significant challenge. We introduce the Fuzzy MAP EM algorithm, a novel approach that incorporates expert knowledge into the parameter estimation process by enriching the Expectation Maximization (EM) framework with fuzzy pseudo-counts derived from an expert-defined fuzzy model. This integration naturally reformulates the problem as a Maximum A Posteriori (MAP) estimation, effectively guiding learning in environments with limited data. In synthetic medical simulations, our method consistently outperforms the standard EM algorithm under both low-data and high-noise conditions. Furthermore, a case study on Myasthenia Gravis illustrates the ability of the Fuzzy MAP EM algorithm to recover a clinically coherent POMDP, demonstrating its potential as a practical tool for data-efficient modeling in healthcare.

I N T R O D U C T I O N T h e I r a n i a n l e o p a r d ( P a n t h e r a p a rd u s t u l l i a n a), a subspecies of the P ersian leopard, is critically endangered due to illegal poaching, habitat fragmentation, and h u m a n - w i l d l i f e c o n f l i c t. C o n s e r v a t i o n e f f o r t s a r e i n c r e a s i n g l y t u r n i n g t o t e c h n o l o g y f o r i n n o v a t i v e m o n i t o r i n g a n d i n t e r v e n t i o n m e t h o d s . Metric 10 Agents T raining Time (hrs) Memor y Usage (GB) CPU Utilization (%) GPU Utilization (%) T raining Time Increase (%) Memor y Usage Increase (%) 5.2 4.5 65 45 - - 20 Agents 50 Agents 6.3 5.1 75 55 20 15 8.0 6.8 85 70 53 51 T able 4. P ercentage of High-Risk zones Covered by Each Method (Mean std) F igure 3. P oacher Detection R ate Across Episodes. Higher Entropy Indicates More Diverse Exploration T able 5. KL Divergence between Inferred q(z) and Ground T ruth T ask Distribution T h e E M - b a s e d p o l i c y e x h i b i t s a n i n i t i a l l y h i g h e n t r o p y, e n c o u r a g i n g d i v e r s e a c t i o n s a m p l i n g, a n d g r a d u a l l y an n e a l s as th e po l i c y be c o m e s co n f i d e n t . Metric Cooperative Coverage Number of Agents Involved Coverage Efficiency (%) P oa ch er D et ec ti on R at e (%) Collision Incidents 6 85.3 - 0 P oacher Detection Coordination Conflict A voidance 8 - 92.1 0 10 - - 0 It enables conser vationists and security forces to allocate limited resources more effectiv e l y a n d a c t i n r e a l t i m e b a s e d o n a c t i o n a b l e i n t e l l i g e n c e d e r i v e d f r o m a u t o n o m o u s a g e n t s .

Neural Information Processing Systems http://nips.cc/

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs with fixed kernel matrices. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.

When the forward model is unknown, or imperfect, artifacts due to model mismatch occur in the recovery of the source.

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard [1]. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix [2], or learning weights for a linear combination of DPPs with fixed kernel matrices [3]. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs with fixed kernel matrices. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure.

We propose a novel deep clustering method that integrates Variational Autoencoders (VAEs) into the Expectation-Maximization (EM) framework. Our approach models the probability distribution of each cluster with a VAE and alternates between updating model parameters by maximizing the Evidence Lower Bound (ELBO) of the log-likelihood and refining cluster assignments based on the learned distributions. This enables effective clustering and generation of new samples from each cluster. Unlike existing VAE-based methods, our approach eliminates the need for a Gaussian Mixture Model (GMM) prior or additional regularization techniques. Experiments on MNIST and FashionMNIST demonstrate superior clustering performance compared to state-of-the-art methods.