Partial Prior Information Research Articles

IRS aided visible light positioning with a single LED transmitter

We propose a visible light positioning (VLP) system with a single light emitting diode (LED) transmitter and an intelligent reflecting surface (IRS) for estimating the position of a receiver equipped with a single photo-detector. By performing a number of transmissions from the LED transmitter and optimizing the orientation vectors of the IRS elements for each transmission, position information is extracted by the receiver based on power measurements of the signals reflecting from the IRS. The theoretical limit and the maximum likelihood (ML) estimator are presented for the proposed setting. In addition, an algorithm, named IRS focusing, is proposed for determining the orientations of the IRS elements during the localization process. The effectiveness of the proposed localization approach is demonstrated through simulations. Furthermore, extensions are provided to apply the proposed approach in the presence of partial prior information about the receiver position and when the IRS is located at the LED transmitter.

GLDADec: marker-gene guided LDA modeling for bulk gene expression deconvolution.

Inferring cell type proportions from bulk transcriptome data is crucial in immunology and oncology. Here, we introduce guided LDA deconvolution (GLDADec), a bulk deconvolution method that guides topics using cell type-specific marker gene names to estimate topic distributions for each sample. Through benchmarking using blood-derived datasets, we demonstrate its high estimation performance and robustness. Moreover, we apply GLDADec to heterogeneous tissue bulk data and perform comprehensive cell type analysis in a data-driven manner. We show that GLDADec outperforms existing methods in estimation performance and evaluate its biological interpretability by examining enrichment of biological processes for topics. Finally, we apply GLDADec to The Cancer Genome Atlas tumor samples, enabling subtype stratification and survival analysis based on estimated cell type proportions, thus proving its practical utility in clinical settings. This approach, utilizing marker gene names as partial prior information, can be applied to various scenarios for bulk data deconvolution. GLDADec is available as an open-source Python package at https://github.com/mizuno-group/GLDADec.

A novel probabilistic source apportionment approach: Bayesian auto-correlated matrix factorization

Abstract. The concentrations of atmospheric particulate matter and many of its constituents are temporally auto-correlated. However, this information has not been utilized in source apportionment methods. Here, we present a Bayesian matrix factorization model (BAMF) that considers the temporal auto-correlation of the components (sources) and provides a direct error estimation. The performance of BAMF is compared with positive matrix factorization (PMF) using synthetic Time-of-Flight Aerosol Chemical Speciation Monitor data, representing different urban environments from typical European towns to megacities. We find that BAMF resolves sources with overall higher factorization performance (temporal behavior and bias) than PMF on all datasets with temporally auto-correlated components. Highly correlated components continue to be challenging and ancillary information is still required to reach good factorizations. However, we demonstrate that adding even partial prior information about the chemical composition of the components to BAMF improves the factorization. Overall, BAMF-type models are promising tools for source apportionment and merit further research.

NEURALGENE: INFERRING GENE REGULATION AND CELL-FATE DYNAMICS FROM NEURAL ODES

In biology, cell-fate decisions are controlled by complex gene regulation. Although gene expression data may be collected at multiple time points, it remains difficult to construct the continuous dynamics from the data. In this work, we developed a data-driven approach, NeuralGene, a model based on neural ordinary differential equations (ODEs), to reconstruct continuous dynamical systems governing gene regulation from temporal gene expression data. In addition, NeuralGene has the flexibility of incorporating partial prior biological information in the model to further improve its accuracy. For a given cell at a static time point, the NeuralGene model can impute its continuous gene expression dynamics and predict its cell fate. We applied NeuralGene to a simulation toggle-switch model to verify its utility in modeling and reconstructing temporal dynamics. In addition, NeuralGene was applied to experimental single-cell qPCR data to show its ability for gene expression imputation and cell-fate prediction.

Target threat estimation based on discrete dynamic Bayesian networks with small samples

The accuracy of target threat estimation has a great impact on command decision-making. The Bayesian network, as an effective way to deal with the problem of uncertainty, can be used to track the change of the target threat level. Unfortunately, the traditional discrete dynamic Bayesian network (DDBN) has the problems of poor parameter learning and poor reasoning accuracy in a small sample environment with partial prior information missing. Considering the finiteness and discreteness of DDBN parameters, a fuzzy k-nearest neighbor (KNN) algorithm based on correlation of feature quantities (CF-FKNN) is proposed for DDBN parameter learning. Firstly, the correlation between feature quantities is calculated, and then the KNN algorithm with fuzzy weight is introduced to fill the missing data. On this basis, a reasonable DDBN structure is constructed by using expert experience to complete DDBN parameter learning and reasoning. Simulation results show that the CF-FKNN algorithm can accurately fill in the data when the samples are seriously missing, and improve the effect of DDBN parameter learning in the case of serious sample missing. With the proposed method, the final target threat assessment results are reasonable, which meets the needs of engineering applications.

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis.

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than . We show that our analytic expressions reproduce the p-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as an energy versus entropy competition.

Satellite derived bathymetry based on ICESat-2 diffuse attenuation signal without prior information

Bathymetric information is critical for environmental monitoring and maintenance of marine safety. The signal received by passive optical remote sensors contains the reflectance information from the seabed, which then forms the informational basis of bathymetry; however, passive optical bathymetry models often require partial prior information. Although spaceborne active lidar has been shown to accurately detect bathymetry within narrow range of tracks, for some small islands or coastal sites, these tracks may not accurately traverse the shallow ocean area. To this end, a satellite derived bathymetry method based on ICESat-2 diffuse attenuation signal without prior information was proposed here. The diffuse attenuation coefficients of the water column were estimated according to the ICESat-2 lidar signal of deep areas near the target shallow water area, and the parameters for the bathymetry algorithm without prior depth information were obtained. Combined with the Sentinel-2 multispectral imagery, accurate large-scale bathymetric information of Zhongye Island and Reefs, Guam, and Ngau were obtained. Bathymetric data from ICESat-2 of multiple tracks were used for verification, and the results showed that the new model performed well, as mean absolute error (MAE) for the three study areas ranged 0.35–1.52 m, and root Mean square error (RMSE) fell between 0.74 and 1.89 m. In the absence of any bathymetric information, the new method can achieve higher or similar accuracy to the more commonly employed Stumpf model.

Metacognitive judgments can potentiate new learning: The role of covert retrieval

Interim tests of previously studied information can potentiate subsequent learning of new information, in part, because retrieval-based processes help to reduce proactive interference from previously learned information. We hypothesized that an effect similar to this forward testing effect would also occur when making judgments of (prior) learning (JOLs). Previous research showed that making JOLs likely prompts covert retrieval attempts and thereby enhances memory, specifically when providing only parts of previously studied information. This study examined the forward effect of different types of JOLs (i.e., with complete or partial prior study information available) on subsequent learning of new materials, compared to restudy and retrieval practice. In a between-subjects design, participants (N = 161) consecutively studied five lists of 20 words with the aim to recall as many of them on a final cumulative recall test. After the presentation of each of the first four lists, participants either restudied the list, made JOLs with complete words, made JOLs with word stems, or they were tested on word stems. Compared to restudy, practicing retrieval and making JOLs with word stems, but not JOLs with complete words, facilitated the List-5 interim recall performance and attenuated the number of intrusions from prior lists. The findings suggest that, similar to overt retrieval, making JOLs with incomplete information can enhance new learning to the extent that it elicits covert retrieval attempts.

Vulnerability Assessment Method for Electronic Devices Excited by Transient Electromagnetic Disturbances

Vulnerability assessment of electronic devices excited by various transient electromagnetic disturbances (TEDs) has been a key issue in electromagnetic susceptibility research. This paper proposes a generalized vulnerability assessment method that includes acquiring data and building assessment model. The data is normally acquired by carrying out experiments, while the assessment model is mainly determined by prior information. As different devices under test (DUTs) could offer a different amount of prior information, a generalized assessment model consisting of a white-box model, a grey-box model, and a black-box model is built to deal with situations of sufficient prior information, partial prior information, and no prior information, respectively.

Recovery analysis for ℓ2/ℓ1−2 minimization via prior support information

This paper discusses the block sparse signal recovery when the partial prior support information is available. A high order block RIP condition for our proposed weighted ℓ2/ℓ1−2 minimization is established, which in absence of support information is proved to improve the previous one. We demonstrate that the obtained recovery condition is weaker than the analogous one for ℓ2/ℓ1−2 minimization if at least 50% of the estimated block support information is accurate, and the corresponding recovery error estimate is also better. In addition, a series of numerical experiments are carried out to show the excellent recovery performance of the weighted ℓ2/ℓ1−2 minimization.

Agnostic Dolinar receiver for coherent-state classification

We consider the problem of discriminating quantum states, where the task is to distinguish two different quantum states with a complete classical knowledge about them, and the problem of classifying quantum states, where the task is to distinguish two classes of quantum states where no prior classical information is available but a finite number of physical copies of each class is given. In the case the quantum states are represented by coherent states of light, we identify intermediate scenarios where partial prior information is available. We evaluate an analytical expression for the minimum error when the quantum states are opposite and a prior on the amplitudes is known. Such a threshold is attained by complex positive operator-valued measurements that involve a highly nonlinear optical procedure. A suboptimal procedure that can be implemented with current technology is presented that is based on a modification of the conventional Dolinar receiver. We study and compare the performance of the scheme under different assumptions on the prior information available.

Application of three-dimensional electrical resistivity tomography in urban zones by arbitrary electrode distribution survey design

One of the most widely used geophysical surveying techniques in the urban environment is the electrical resistivity tomography (ERT) method. However, traditional ERT can only utilize regular grid and equidistant electrode layouts. Furthermore, all electrodes must be connected by long cables, and the existence of obstacles in urban environments makes it challenging to implement such layouts. We therefore present an optimized 3D ERT survey design consisting of arbitrarily distributed electrodes. We use the dipole-dipole array as the data acquisition unit. Each unit is independent and can be randomly distributed and adjusted in length. The unit can be used as a current or potential electrode as required. In this way, the limitations of grids and cables can be eliminated. Arbitrary distribution does not mean doing whatever you want. Must follow the basic principles of the geoelectric method. Based on this, we have formulated a set of reasonable procedures in the survey design, including the ‘main-sub unit’ and the ‘effective measurement circle’, which make the surveying system run more quickly and accurately. We select a complex urban area with partial prior information as the field sample to verify our survey design. This approach can effectively avoid the disadvantages of the traditional ERT method and obtain correct and effective results in a complex urban environment.

A Gibbs Sampler for a Class of Random Convex Polytopes

We present a Gibbs sampler for the Dempster–Shafer (DS) approach to statistical inference for categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields three-valued uncertainty assessments representing probabilities “for,” “against,” and “don’t know” about formal assertions of interest. The proposed algorithm targets the distribution of a class of random convex polytopes which encapsulate the DS inference. The sampler relies on an equivalence between the iterative constraints of the vertex configuration and the nonnegativity of cycles in a fully connected directed graph. Illustrations include the testing of independence in 2 × 2 contingency tables and parameter estimation of the linkage model.

New RIP Bounds for Recovery of Sparse Signals With Partial Support Information via Weighted ${\ell_{p}}$ -Minimization

In this paper, we consider the recovery of $k$ -sparse signals using the weighted $\ell _{p}$ ( $0 ) minimization when some partial prior information on the support is available. First, we present a unified analysis of restricted isometry constant $\delta _{tk}$ with $d ( $d \geqslant 1$ is determined by the prior support information) for sparse signal recovery by the weighted $\ell _{p}$ ( $0 ) minimization in both noiseless and noisy settings. This result fills a vacancy on $\delta _{tk}$ with $t , compared with previous works on $\delta _{(a+1)k}$ ( $a>1$ ). Second, we provide a sufficient condition on $\delta _{tk}$ with $1 for the recovery of sparse signals using the $\ell _{p}$ ( $0 ) minimization, which extends the existing optimal result on $\delta _{2k}$ in the literature. Last, various numerical examples are presented to demonstrate the better performance of the weighted $\ell _{p}$ ( $0 ) minimization is achieved when the accuracy of prior information on the support is at least 50%, compared with that of the $\ell _{p}$ ( $0 ) minimization.

Sequential process to choose efficient sampling design based on partial prior information data and simulations

Issues on sampling procedure definition led numerous study results to be biased and object of controversy. Choosing relevant sampling design and number of samples is a difficult task when wanted to set up or optimize a survey. The survey design choice is very important to avoid bias and increase the survey cost-efficiency. It can have a strong effect on the sample size needed to achieve some targeted accuracy on results. And on the final cost of the procedure.The sequential process we expose here melt design based and model based sampling theories. Its objectives are helping practitioners defining a sampling design and a number of samples for their survey when inference to the whole population is wanted. The main idea is to mathematically reconstruct the distribution of the surveyed population. Then assess and compare cost-effectiveness of various sampling designs on this population. This process allows setting predetermined level(s) of accuracy to be reached in the targeted estimates and to take into account previous relevant data. Results are an optimal sampling design and an associated optimal sample size for a desired accuracy in the results. This accuracy is so achieved without excess sampling. Strength of this process is that it is based on simulations. This allows trying a high number of combinations between sampling design, sample size and desired level of accuracy. Sampling design performances can thus be compared.The user can decide which combination is the best for his survey and apply it for real. We discuss how to use available data to improve the survey, from the case were several historical data are provided to the case where no data are available.

An active reconstruction algorithm based on partial prior information

Active reconstruction is an intelligent perception method that achieves object modeling with few views and short motion paths by systematically adjusting the parameters of the camera while ensuring model integrity. Part of the object information is always known for vision tasks in real scenes, and it provides some guidance for the view planning. A two-step active reconstruction algorithm based on partial prior information is presented, which includes rough shape estimation phase and complete object reconstruction phase, and both of them introduce the concept of active vision. An information expression method is proposed that can be used to manually initialize the repository according to specific visual tasks, and then the prior information and detected information are used to plan the next best view online until the object reconstruction is completed. The method is evaluated with simulated experiments and the result is compared with other methods.

Semi-Clairvoyant Scheduling in Data Analytics Systems

Popular data analytics systems including Apache Hadoop, Dryad, and Apache Spark abstract jobs as directed acyclic graphs (DAGs). Speeding up completions for DAG jobs matter in practice in order to support real-time decisions. State-of-the-art works propose clairvoyant schedulers to optimize these goals, however, they assume complete job information as a prior knowledge which includes the precise DAG structure, and fine-grained resource requirement and duration time of each task. This assumption limits their applicability. In this paper, to be more practical, we relax the complete prior knowledge assumption and rely solely on partial prior information, based on which, we design a semi-clairvoyant task scheduler Cobra operating within each job. When managing resources for a job, Cobra adaptively adjusts its resource desires in a multiplicative-increase multiplicative-decrease manner on the basis of the its current resource utilization and the presence of current waiting tasks. When assigning tasks to run on the allocated resources, Cobra strives to satisfy task locality preference by tolerating each task waiting for some time that is bounded by a parameterized threshold. Even with the partial prior job information, when a set of jobs in which each employing Cobra as its task scheduler, run on a cluster that employs the fair job scheduler, we theoretically prove the produced makespan and average job response time are O(1)-competitive in different settings. We implement our design in Spark on YARN system, and use experiments from both real deployments and simulations on Google's trace to verify the performance promotion and sensitivity of Cobra.

Optimal Universal Learning Machines for Quantum State Discrimination

We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by $n$ qubits prepared in the first template state and by $n$ more qubits prepared in the second template state. In this situation we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size $n$ of the training data. Finite size corrections around the asymptotic limit $n\rightarrow \infty$ are also derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems.

An Optimal Recovery Condition for Sparse Signals with Partial Support Information via OMP

This paper considers the orthogonal matching pursuit (OMP) algorithm for sparse recovery in both noiseless and noisy cases when the partial prior information is available. The prior information is included in an estimated subset of the support of the sparse signal. First, we show that if $$\varvec{A}$$ satisfies $$\delta _{k+b+1}<\frac{1}{\sqrt{k-g+1}}$$ , then the OMP algorithm can perfectly recover any k-sparse signal $$\varvec{x}$$ from $$\varvec{y}=\varvec{Ax}$$ in $$k-g$$ iterations when the prior support of $$\varvec{x}$$ includes g true indices and b wrong indices. Furthermore, we show that the condition $$\delta _{k+b+1}<\frac{1}{\sqrt{k-g+1}}$$ is optimal. Second, we achieve the exact recovery of the remainder support (i.e., it is composed of indices in the true support of $$\varvec{x}$$ but not in the prior support) from $$\varvec{y}=\varvec{Ax}+\varvec{v}$$ under appropriate conditions. On the other hand, for the remainder support recovery, we also obtain a necessary condition based on the minimum magnitude of nonzero elements in the remainder support of $$\varvec{x}$$ . Compared to the OMP algorithm, numerical experiments demonstrate that the OMP algorithm with the partial prior information has better recovery performance.

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors.

Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter but the prior information is in a subparameter linear function of , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.