The initial interaction of a user with a recommender system is problematic because, in such a so-called cold start situation, the recommender system has very little information about the user, if any. Moreover, in collaborative filtering, users need to share their preferences with the service provider by rating items while in content-based filtering there is no need for such information sharing. We have recently shown that a content-based model that uses hypercube graphs can determine user preferences with a very limited number of ratings while better preserving user privacy. In this paper, we confirm these findings on the basis of experiments with more than 1,000 users in the restaurant and movie domains. We show that the proposed method outperforms standard machine learning algorithms when the number of available ratings is at most 10, which often happens, and is competitive with larger training sets. In addition, training is simple and does not require large computational efforts.
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In many practical control applications, the performance level of a closed-loop system degrades over time due to the change of plant characteristics. Thus, there is a strong need for redesigning a controller without going through the system modeling process, which is often difficult for closed-loop systems. Reinforcement learning (RL) is one of the promising approaches that enable model-free redesign of optimal controllers for nonlinear dynamical systems based only on the measurement of the closed-loop system. However, the learning process of RL usually requires a considerable number of trial-and-error experiments using the poorly controlled system that may accumulate wear on the plant. To overcome this limitation, we propose a model-free two-step design approach that improves the transient learning performance of RL in an optimal regulator redesign problem for unknown nonlinear systems. Specifically, we first design a linear control law that attains some degree of control performance in a model-free manner, and then, train the nonlinear optimal control law with online RL by using the designed linear control law in parallel. We introduce an offline RL algorithm for the design of the linear control law and theoretically guarantee its convergence to the LQR controller under mild assumptions. Numerical simulations show that the proposed approach improves the transient learning performance and efficiency in hyperparameter tuning of RL.
The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of tau, the between-study standard deviation, and the shrunken estimates of the study effects as a function of tau. With a small or moderate number of studies, tau is not estimated with much precision, and parameter estimates and shrunken study effect estimates can vary widely depending on the correct value of tau. The trace plot allows visualization of the sensitivity to tau along with a plot that shows which values of tau are plausible and which are implausible. A comparable frequentist or empirical Bayes version provides similar results. The concepts are illustrated using examples in meta-analysis and meta-regression; implementaton in R is facilitated in a Bayesian or frequentist framework using the bayesmeta and metafor packages, respectively.
Many approaches have been proposed to use diffusion models to augment training datasets for downstream tasks, such as classification. However, diffusion models are themselves trained on large datasets, often with noisy annotations, and it remains an open question to which extent these models contribute to downstream classification performance. In particular, it remains unclear if they generalize enough to improve over directly using the additional data of their pre-training process for augmentation. We systematically evaluate a range of existing methods to generate images from diffusion models and study new extensions to assess their benefit for data augmentation. Personalizing diffusion models towards the target data outperforms simpler prompting strategies. However, using the pre-training data of the diffusion model alone, via a simple nearest-neighbor retrieval procedure, leads to even stronger downstream performance. Our study explores the potential of diffusion models in generating new training data, and surprisingly finds that these sophisticated models are not yet able to beat a simple and strong image retrieval baseline on simple downstream vision tasks.
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is necessary to create algorithms that can take into account both, the physical mechanisms responsible for generating these measurements and the intrinsic characteristics of the images being analyzed. In this work, the sparse representation of images is reviewed, which is a realistic, compact and effective generative model for natural images inspired by the visual system of mammals. It enables us to address ill-posed linear inverse problems by training the model on a vast collection of images. Moreover, we extend the application of sparse coding to solve the non-linear and ill-posed problem in microwave tomography imaging, which could lead to a significant improvement of the state-of-the-arts algorithms.
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings directly depends on how much the geometry of the continuous space matches the graph structure. Manifolds are mathematical structure that can enable to incorporate in their topological spaces the graph characteristics, and in particular nodes distances. State-of-the-art of manifold-based graph embedding algorithms take advantage of the assumption that the projection on a tangential space of each point in the manifold (corresponding to a node in the graph) would locally resemble a Euclidean space. Although this condition helps in achieving efficient analytical solutions to the embedding problem, it does not represent an adequate set-up to work with modern real life graphs, that are characterized by weighted connections across nodes often computed over sparse datasets with missing records. In this work, we introduce a new class of manifold, named soft manifold, that can solve this situation. In particular, soft manifolds are mathematical structures with spherical symmetry where the tangent spaces to each point are hypocycloids whose shape is defined according to the velocity of information propagation across the data points. Using soft manifolds for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets. Experimental results on reconstruction tasks on synthetic and real datasets show how the proposed approach enable more accurate and reliable characterization of graphs in continuous spaces with respect to the state-of-the-art.
Regression with random data objects is becoming increasingly common in modern data analysis. Unfortunately, like the traditional regression setting with Euclidean data, random response regression is not immune to the trouble caused by unusual observations. A metric Cook's distance extending the classical Cook's distances of Cook (1977) to general metric-valued response objects is proposed. The performance of the metric Cook's distance in both Euclidean and non-Euclidean response regression with Euclidean predictors is demonstrated in an extensive experimental study. A real data analysis of county-level COVID-19 transmission in the United States also illustrates the usefulness of this method in practice.
Optical computing systems provide high-speed and low-energy data processing but face deficiencies in computationally demanding training and simulation-to-reality gaps. We propose a model-free optimization (MFO) method based on a score gradient estimation algorithm for computationally efficient in situ training of optical computing systems. This approach treats an optical computing system as a black box and back-propagates the loss directly to the optical computing weights' probability distributions, circumventing the need for a computationally heavy and biased system simulation. Our experiments on a single-layer diffractive optical computing system show that MFO outperforms hybrid training on the MNIST and FMNIST datasets. Furthermore, we demonstrate image-free and high-speed classification of cells from their phase maps. Our method's model-free and high-performance nature, combined with its low demand for computational resources, expedites the transition of optical computing from laboratory demonstrations to real-world applications.
Causal mediation analysis aims to investigate how an intermediary factor, called a mediator, regulates the causal effect of a treatment on an outcome. With the increasing availability of measurements on a large number of potential mediators, methods for selecting important mediators have been proposed. However, these methods often assume the absence of unmeasured mediator-outcome confounding. We allow for such confounding in a linear structural equation model for the outcome and further propose an approach to tackle the mediator selection issue. To achieve this, we firstly identify causal parameters by constructing a pseudo proxy variable for unmeasured confounding. Leveraging this proxy variable, we propose a partially penalized method to identify mediators affecting the outcome. The resultant estimates are consistent, and the estimates of nonzero parameters are asymptotically normal. Motivated by these results, we introduce a two-step procedure to consistently select active mediation pathways, eliminating the need to test composite null hypotheses for each mediator that are commonly required by traditional methods. Simulation studies demonstrate the superior performance of our approach compared to existing methods. Finally, we apply our approach to genomic data, identifying gene expressions that potentially mediate the impact of a genetic variant on mouse obesity.
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case of duality between the diffusion and a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox-Ingersoll-Ross and Wright-Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.
In an acceptance monitoring system, acceptance sampling techniques are used to increase production, enhance control, and deliver higher-quality products at a lesser cost. It might not always be possible to define the acceptance sampling plan parameters as exact values, especially, when data has uncertainty. In this work, acceptance sampling plans for a large number of identical units with exponential lifetimes are obtained by treating acceptable quality life, rejectable quality life, consumer's risk, and producer's risk as fuzzy parameters. To obtain plan parameters of sequential sampling plans and repetitive group sampling plans, fuzzy hypothesis test is considered. To validate the sampling plans obtained in this work, some examples are presented. Our results are compared with existing results in the literature. Finally, to demonstrate the application of the resulting sampling plans, a real-life case study is presented.
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