Computation of the maximum likelihood estimator in low-rank factor analysis

Khamaru, Koulik; Mazumder, Rahul

doi:10.1007/s10107-019-01370-7

Cited by 8 publications

(4 citation statements)

References 32 publications

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“…Clearly, R 1 (Φ i ) and R 2 (Φ i ) are both concave functions, but their difference is not concave. Khamaru and Mazumder in [46] propose a global lower-bound…”

Section: B Alternating Optimization Algorithmmentioning

confidence: 99%

Multi-Channel Factor Analysis With Common and Unique Factors

Ramírez

Santamarı́a

Scharf

et al. 2020

IEEE Trans. Signal Process.

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This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.

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“…Clearly, R 1 (Φ i ) and R 2 (Φ i ) are both concave functions, but their difference is not concave. Khamaru and Mazumder in [46] propose a global lower-bound…”

Section: B Alternating Optimization Algorithmmentioning

confidence: 99%

Multi-Channel Factor Analysis With Common and Unique Factors

Ramírez

Santamarı́a

Scharf

et al. 2020

IEEE Trans. Signal Process.

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show abstract

“…Recently, a majorization-minimization (MM) [12] based method has been proposed in [4] to obtain the optimal Σ. Plugging the optimal B ⋆ from Lemma 1 in (1), we can achieve a concentrated version of (1).…”

Section: Algorithmmentioning

confidence: 99%

“…Plugging the optimal B ⋆ from Lemma 1 in (1), we can achieve a concentrated version of (1). 4,5]. Then the update of Φ can be easily obtained as φ…”

Section: Algorithmmentioning

confidence: 99%

Robust Factor Analysis Parameter Estimation

Zhou

Liu

Kumar

et al. 2020

Lecture Notes in Computer Science

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This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor analysis (FA). By assuming the observed data to follow the multivariate Student's t distribution, we can robustly estimate the parameters via maximum likelihood estimation (MLE). However, the MLE of parameters becomes an intractable problem when the multivariate Student's t distribution and the FA structure are both introduced. In this paper, we propose an algorithm based on the generalized expectation maximization (GEM) method to obtain estimators. The robustness of our proposed method is further enhanced to cope with missing values. Finally, we show the performance of our proposed algorithm using both synthetic data and real financial data.

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“…In the logistic regression function, the maximum likelihood function is applied to obtain the parameters of the model. en, a logistic regression model is constructed, which is turned into an optimization problem using the loglikelihood function [34]. During the period of learning the logistic regression model, the gradient descent method or other improved scores is usually used [35].…”

Section: Experimental Analysis Using Logistic Regressionmentioning

confidence: 99%

Mushroom Toxicity Recognition Based on Multigrained Cascade Forest

Wang

Yang

2020

Scientific Programming

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Due to the tastiness of mushroom, this edible fungus often appears in people’s daily meals. Nevertheless, there are still various mushroom species that have not been identified. Thus, the automatic identification of mushroom toxicity is of great value. A number of methods are commonly employed to recognize mushroom toxicity, such as folk experience, chemical testing, animal experiments, and fungal classification, all of which cannot produce quick, accurate results and have a complicated cycle. To solve these problems, in this paper, we proposed an automatic toxicity identification method based on visual features. The proposed method regards toxicity identification as a binary classification problem. First, intuitive and easily accessible appearance data, such as the cap shape and color of mushrooms, were taken as features. Second, the missing data in any of the features were handled in two ways. Finally, three pattern-recognition methods, including logistic regression, support vector machine, and multigrained cascade forest, were used to construct 3 different toxicity classifiers for mushrooms. Compared with the logistic regression and support vector machine classifiers, the multigrained cascade forest classifier had better performance with an accuracy of approximately 98%, enhancing the possibility of preventing food poisoning. These classifiers can recognize the toxicity of mushrooms—even that of some unknown species—according to their appearance features and important social and application value.

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Computation of the maximum likelihood estimator in low-rank factor analysis

Cited by 8 publications

References 32 publications

Multi-Channel Factor Analysis With Common and Unique Factors

Multi-Channel Factor Analysis With Common and Unique Factors

Robust Factor Analysis Parameter Estimation

Mushroom Toxicity Recognition Based on Multigrained Cascade Forest

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