Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow. However, these algorithms require an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a deep neural network policy.
Deep learning techniques have been used to build velocity models (VMs) for seismic traveltime tomography and have shown encouraging performance in recent years. However, they need to generate labeled samples (i.e., pairs of input and label) to train the deep neural network (NN) with end-to-end learning, and the real labels for field data inversion are usually missing or very expensive. Some traditional tomographic methods can be implemented quickly, but their effectiveness is often limited by prior assumptions. To avoid generating and/or collecting labeled samples, we propose a novel method by integrating deep learning and dictionary learning to enhance the VMs with low resolution by using the traditional tomography-least square method (LSQR). We first design a type of shallow and simple NN to reduce computational cost followed by proposing a two-step strategy to enhance the VMs with low resolution: (1) Warming up. An initial dictionary is trained from the estimation by LSQR through dictionary learning method; (2) Dictionary optimization. The initial dictionary obtained in the warming-up step will be optimized by the NN, and then it will be used to reconstruct high-resolution VMs with the reference slowness and the estimation by LSQR. Furthermore, we design a loss function to minimize traveltime misfit to ensure that NN training is label-free, and the optimized dictionary can be obtained after each epoch of NN training. We demonstrate the effectiveness of the proposed method through the numerical tests on both synthetic and field data.
Dictionary learning (DL) is commonly used in computational biology to tackle ubiquitous clustering problems due to its conceptual simplicity and relatively low computational complexity. However, DL algorithms produce results that lack interpretability and are not optimized for large-scale graph-structured data. We propose a novel DL algorithm called online convex network dictionary learning (online cvxNDL) that can handle extremely large datasets and enables the interpretation of dictionary elements, which serve as cluster representatives, through convex combinations of real measurements. Moreover, the algorithm can be applied to network-structured data via specialized subnetwork sampling techniques. To demonstrate the utility of our approach, we apply cvxNDL on 3D-genome RNAPII ChIA-Drop data to identify important long-range interaction patterns. ChIA-Drop probes higher-order interactions, and produces hypergraphs whose nodes represent genomic fragments. The hyperedges represent observed physical contacts. Our hypergraph model analysis creates an interpretable dictionary of long-range interaction patterns that accurately represent global chromatin physical contact maps. Using dictionary information, one can also associate the contact maps with RNA transcripts and infer cellular functions. Our results offer two key insights. First, we demonstrate that online cvxNDL retains the accuracy of classical DL methods while simultaneously ensuring unique interpretability and scalability. Second, we identify distinct collections of proximal and distal interaction patterns involving chromatin elements shared by related processes across different chromosomes, as well as patterns unique to specific chromosomes. To associate the dictionary elements with biological properties of the corresponding chromatin regions, we employ Gene Ontology enrichment analysis and perform RNA coexpression studies.
We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used $\ell_{2,1}$ regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.
Multiple Instance Learning (MIL) has been widely used in weakly supervised whole slide image (WSI) classification. Typical MIL methods include a feature embedding part, which embeds the instances into features via a pre-trained feature extractor, and an MIL aggregator that combines instance embeddings into predictions. Most efforts have typically focused on improving these parts. This involves refining the feature embeddings through self-supervised pre-training as well as modeling the correlations between instances separately. In this paper, we proposed a sparsely coding MIL (SC-MIL) method that addresses those two aspects at the same time by leveraging sparse dictionary learning. The sparse dictionary learning captures the similarities of instances by expressing them as sparse linear combinations of atoms in an over-complete dictionary. In addition, imposing sparsity improves instance feature embeddings by suppressing irrelevant instances while retaining the most relevant ones. To make the conventional sparse coding algorithm compatible with deep learning, we unrolled it into a sparsely coded module leveraging deep unrolling. The proposed SC module can be incorporated into any existing MIL framework in a plug-and-play manner with an acceptable computational cost. The experimental results on multiple datasets demonstrated that the proposed SC module could substantially boost the performance of state-of-the-art MIL methods. The codes are available at \href{https://github.com/sotiraslab/SCMIL.git}{https://github.com/sotiraslab/SCMIL.git}.
Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor $\boldsymbol{h} \in \mathbb{R}^{C \times T \times d}$. Given embedding vector $\boldsymbol{h}_{c,t} \in \mathbb{R}^d$ at sequence position $t \le T$ in a sequence (or context) $c \le C$, extracting the mean effects yields the decomposition \[ \boldsymbol{h}_{c,t} = \boldsymbol{\mu} + \mathbf{pos}_t + \mathbf{ctx}_c + \mathbf{resid}_{c,t} \] where $\boldsymbol{\mu}$ is the global mean vector, $\mathbf{pos}_t$ and $\mathbf{ctx}_c$ are the mean vectors across contexts and across positions respectively, and $\mathbf{resid}_{c,t}$ is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) $(\mathbf{pos}_t)_{t}$ forms a low-dimensional, continuous, and often spiral shape across layers, (2) $(\mathbf{ctx}_c)_c$ shows clear cluster structure that falls into context topics, and (3) $(\mathbf{pos}_t)_{t}$ and $(\mathbf{ctx}_c)_c$ are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.
This paper seeks to solve Multi-Source Domain Adaptation (MSDA), which aims to mitigate data distribution shifts when transferring knowledge from multiple labeled source domains to an unlabeled target domain. We propose a novel MSDA framework based on dictionary learning and optimal transport. We interpret each domain in MSDA as an empirical distribution. As such, we express each domain as a Wasserstein barycenter of dictionary atoms, which are empirical distributions. We propose a novel algorithm, DaDiL, for learning via mini-batches: (i) atom distributions; (ii) a matrix of barycentric coordinates. Based on our dictionary, we propose two novel methods for MSDA: DaDil-R, based on the reconstruction of labeled samples in the target domain, and DaDiL-E, based on the ensembling of classifiers learned on atom distributions. We evaluate our methods in 3 benchmarks: Caltech-Office, Office 31, and CRWU, where we improved previous state-of-the-art by 3.15%, 2.29%, and 7.71% in classification performance. Finally, we show that interpolations in the Wasserstein hull of learned atoms provide data that can generalize to the target domain.
In this paper, we advocate for using large pre-trained monolingual language models in cross lingual zero-shot word sense disambiguation (WSD) coupled with a contextualized mapping mechanism. We also report rigorous experiments that illustrate the effectiveness of employing sparse contextualized word representations obtained via a dictionary learning procedure. Our experimental results demonstrate that the above modifications yield a significant improvement of nearly 6.5 points of increase in the average F-score (from 62.0 to 68.5) over a collection of 17 typologically diverse set of target languages. We release our source code for replicating our experiments at https://github.com/begab/sparsity_makes_sense.
In this paper we present new methods of anomaly detection based on Dictionary Learning (DL) and Kernel Dictionary Learning (KDL). The main contribution consists in the adaption of known DL and KDL algorithms in the form of unsupervised methods, used for outlier detection. We propose a reduced kernel version (RKDL), which is useful for problems with large data sets, due to the large kernel matrix. We also improve the DL and RKDL methods by the use of a random selection of signals, which aims to eliminate the outliers from the training procedure. All our algorithms are introduced in an anomaly detection toolbox and are compared to standard benchmark results.
In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large. There are several ways of reducing the kernel size, notably Nystr\"om sampling. We propose here a method more in the spirit of dictionary learning, where the kernel vectors are obtained with a trained sparse representation of the input signals. Moreover, we optimize directly the kernel vectors in the KDL process, using gradient descent steps. We show with three data sets that our algorithms are able to provide better representations, despite using a small number of kernel vectors, and also decrease the execution time with respect to KDL.
In this paper we present a new classification method based on Dictionary Learning (DL). The main contribution consists of a kernel version of incoherent DL, derived from its standard linear counterpart. We also propose an improvement of the AK-SVD algorithm concerning the representation update. Our algorithms are tested on several popular databases of classification problems.
Time series data across scientific domains are often collected under distinct states (e.g., tasks), wherein latent processes (e.g., biological factors) create complex inter- and intra-state variability. A key approach to capture this complexity is to uncover fundamental interpretable units within the data, Building Blocks (BBs), which modulate their activity and adjust their structure across observations. Existing methods for identifying BBs in multi-way data often overlook inter- vs. intra-state variability, produce uninterpretable components, or do not align with properties of real-world data, such as missing samples and sessions of different duration. Here, we present a framework for Similarity-driven Building Block Inference using Graphs across States (SiBBlInGS). SiBBlInGS offers a graph-based dictionary learning approach for discovering sparse BBs along with their temporal traces, based on co-activity patterns and inter- vs. intra-state relationships. Moreover, SiBBlInGS captures per-trial temporal variability and controlled cross-state structural BB adaptations, identifies state-specific vs. state-invariant components, and accommodates variability in the number and duration of observed sessions across states. We demonstrate SiBBlInGS's ability to reveal insights into complex phenomena as well as its robustness to noise and missing samples through several synthetic and real-world examples, including web search and neural data.
Nonlocal self-similarity within natural images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the $\ell 1$ sparsity prior of CDLNet to a weighted group-sparsity prior. From this formulation, we propose a novel sliding-window nonlocal operation, enabled by sparse array arithmetic. In addition to competitive performance with black-box nonlocal DNNs, we demonstrate the proposed sliding-window sparse attention enables inference speeds greater than an order of magnitude faster than its competitors.
This article presents a leak localization methodology based on state estimation and learning. The first is handled by an interpolation scheme, whereas dictionary learning is considered for the second stage. The novel proposed interpolation technique exploits the physics of the interconnections between hydraulic heads of neighboring nodes in water distribution networks. Additionally, residuals are directly interpolated instead of hydraulic head values. The results of applying the proposed method to a well-known case study (Modena) demonstrated the improvements of the new interpolation method with respect to a state-of-the-art approach, both in terms of interpolation error (considering state and residual estimation) and posterior localization.
In most image retrieval systems, images include various high-level semantics, called tags or annotations. Virtually all the state-of-the-art image annotation methods that handle imbalanced labeling are search-based techniques which are time-consuming. In this paper, a novel coupled dictionary learning approach is proposed to learn a limited number of visual prototypes and their corresponding semantics simultaneously. This approach leads to a real-time image annotation procedure. Another contribution of this paper is that utilizes a marginalized loss function instead of the squared loss function that is inappropriate for image annotation with imbalanced labels. We have employed a marginalized loss function in our method to leverage a simple and effective method of prototype updating. Meanwhile, we have introduced ${\ell}_1$ regularization on semantic prototypes to preserve the sparse and imbalanced nature of labels in learned semantic prototypes. Finally, comprehensive experimental results on various datasets demonstrate the efficiency of the proposed method for image annotation tasks in terms of accuracy and time. The reference implementation is publicly available on https://github.com/hamid-amiri/MCDL-Image-Annotation.
Cloud K-SVD is a dictionary learning algorithm that can train at multiple nodes and hereby produce a mutual dictionary to represent low-dimensional geometric structures in image data. We present a novel application of the algorithm as we use it to recover both noiseless and noisy images from overlapping patches. We implement a node network in Kubernetes using Docker containers to facilitate Cloud K-SVD. Results show that Cloud K-SVD can recover images approximately and remove quantifiable amounts of noise from benchmark gray-scaled images without sacrificing accuracy in recovery; we achieve an SSIM index of 0.88, 0.91 and 0.95 between clean and recovered images for noise levels ($\mu$ = 0, $\sigma^{2}$ = 0.01, 0.005, 0.001), respectively, which is similar to SOTA in the field. Cloud K-SVD is evidently able to learn a mutual dictionary across multiple nodes and remove AWGN from images. The mutual dictionary can be used to recover a specific image at any of the nodes in the network.
Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.
Most existing convolutional dictionary learning (CDL) algorithms are based on batch learning, where the dictionary filters and the convolutional sparse representations are optimized in an alternating manner using a training dataset. When large training datasets are used, batch CDL algorithms become prohibitively memory-intensive. An online-learning technique is used to reduce the memory requirements of CDL by optimizing the dictionary incrementally after finding the sparse representations of each training sample. Nevertheless, learning large dictionaries using the existing online CDL (OCDL) algorithms remains highly computationally expensive. In this paper, we present a novel approximate OCDL method that incorporates sparse decomposition of the training samples. The resulting optimization problems are addressed using the alternating direction method of multipliers. Extensive experimental evaluations using several image datasets show that the proposed method substantially reduces computational costs while preserving the effectiveness of the state-of-the-art OCDL algorithms.
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning and statistics such as the sparse principal component analysis, sparse spectral clustering, and orthogonal dictionary learning. We propose a Riemannian alternating direction method of multipliers (ADMM) to solve this class of problems. Our algorithm adopts easily computable steps in each iteration. The iteration complexity of the proposed algorithm for obtaining an $\epsilon$-stationary point is analyzed under mild assumptions. Existing ADMM for solving nonconvex problems either does not allow nonconvex constraint set, or does not allow nonsmooth objective function. Our algorithm is the first ADMM type algorithm that minimizes a nonsmooth objective over manifold -- a particular nonconvex set. Numerical experiments are conducted to demonstrate the advantage of the proposed method.
Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, is of increasing importance to applications in signal processing and data science. When the dictionary is known, recovery of $\mathbf{x}_i$ is possible even for sparsity linear in dimension $M$, yet to date, the only algorithms which provably succeed in the linear sparsity regime are Riemannian trust-region methods, which are limited to orthogonal dictionaries, and methods based on the sum-of-squares hierarchy, which requires super-polynomial time in order to obtain an error which decays in $M$. In this work, we introduce SPORADIC (SPectral ORAcle DICtionary Learning), an efficient spectral method on family of reweighted covariance matrices. We prove that in high enough dimensions, SPORADIC can recover overcomplete ($K > M$) dictionaries satisfying the well-known restricted isometry property (RIP) even when sparsity is linear in dimension up to logarithmic factors. Moreover, these accuracy guarantees have an ``oracle property" that the support and signs of the unknown sparse vectors $\mathbf{x}_i$ can be recovered exactly with high probability, allowing for arbitrarily close estimation of $\mathbf{D}$ with enough samples in polynomial time. To the author's knowledge, SPORADIC is the first polynomial-time algorithm which provably enjoys such convergence guarantees for overcomplete RIP matrices in the near-linear sparsity regime.