On Estimation of a Probability Density Function and Mode

By Emanuel Parzen. 1962

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Generating Sentences by Editing Prototypes (2017, background): “From a generative modeling perspective, editing randomly sampled training sentences closely resembles nonparametric kernel density estimation (Parzen, 1962) where one samples points from a training set, and adds noise to smooth the density.”
On the Quantitative Analysis of Decoder-Based Generative Models (2016, methodology): “In order for the likelihood to be well-defined, we follow the same assumption made when evaluating using Kernel Density Estimator [20]: we assume a Gaussian observation model with a fixed variance hyperparameter σ(2).”
Practical Evasion of a Learning-Based Classifier: A Case Study (2014, methodology): “The density function must be estimated beforehand, using the standard techniques of kernel density estimation [34].”
Security analysis of online centroid anomaly detection (2010, background): “…point is considered anomalous if its anomaly score exceeds a fixed threshold r. Centroid anomaly detection can be seen as a special case for the SVDD with outlier fraction η = 1 and of the Parzen window density estimator (Parzen, 1962) with the Gaussian kernel function k(x,y) = 1√ 2π exp(−12x · y).”
Benchmark and Survey of Automated Machine Learning Frameworks (2019, methodology): “Using kernel density estimation (KDE) (Parzen, 1961), those sets are transformed into two distributions.”
Survey on Automated Machine Learning (2019, methodology): “These two distributions are created using kernel density estimations (KDEs) (Parzen, 1961). p(D) is defined as p(D) = ∫ R p(D | f) · p(f) df = γ l(D) + (1− γ)g(D).”
Bayesian Learning of Kernel Embeddings (2016, methodology): “…squared error is a popular choice (Bowman, 1985), and there is even a formula giving the optimal smoothing parameter asymptotically, see Rosenblatt (1956); Parzen (1962)) but we are not aware of work linking this literature to methods based on positive definite/RKHS kernels we study here.”
Verified Uncertainty Calibration (2019, background): “Recalibration is related to (conditional) density estimation [44, 45] as the goal is to estimate E[Y | f(X)].”
Transformation Invariance in Pattern Recognition-Tangent Distance and Tangent Propagation (1996, background): “Output functions range from simply voting the labels associated with the k closest prototypes (K-Nearest Neighbors), to computing a score for each class as a linear combination of the distances to all the prototypes, using xed [21] or learned [5] coe cients.”
Crisp Boundary Detection Using Pointwise Mutual Information (2014, methodology): “We use a nonparametric kernel density estimator [31] since it has high capacity without requiring an increase in feature dimensionality.”
Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models (2017, methodology): “…such as annealed importance sampling (AIS; (Neal 2001; Wu et al. 2017)) and non-parameteric methods such as kernel density estimation (KDE; (Parzen 1962; Goodfellow et al. 2014)) are computationally slow and crucially rely on assumptions of a Gaussian observation model for the likelihood…”
Probability measures on the space of persistence diagrams (2011, methodology): “, yn}, we can use a variation of kernel density estimation [32, 33] to provide the following density estimates for diagrams corresponding to the objects O1 and O2, respectively: p̂(x|O1) = 1 mκτ m ∑”
A versatile and robust metric entropy test of time-reversibility, and other hypotheses (2007, methodology): “For testing the null of serial independence, we employ kernel estimators of f(y, y−j), f(y), and f(y−j), j = 1, 2, . . . ,K originally proposed by Parzen (1962), with likelihood cross-validation used for bandwidth selection leading to density estimators that are “optimal” according to the…”
Object tracking using SIFT features and mean shift (2009, methodology): “Given the sample points and the kernel function kðxÞ, the probability density function (p.d.f.) of the object in the current image can be estimated using kernel density estimation [ 30 ] as”
Decision Forests for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning (2011, methodology): “Popular, non-parametric density estimation techniques are kernelbased algorithms such as the Parzen-Rosenblatt windows estimator [67].”
PROJECTION PURSUIT DENSITY ESTIMATION (1984, methodology): “Examples of successful methods are the related techniques of kernel estimates (Parzen, 1962; Rosenblatt, 1971), near neighbor estimates (Loftsgaarden and Quesenberry, 1965) and splines (Boneva, Kendall, and Stefanov, 1971).”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “…to assuming a parametric model for the pdf pΦ|θ of the summary statistics is to approximate it by a kernel density estimate (Rosenblatt, 1956; Parzen, 1962; Mack and Rosenblatt, 1979; Wand and Jones, 1995), pΦ|θ(φ|θ) ≈ EN [K(φ, Φθ)] , (18) where K is a suitable kernel and EN denotes…”
Simplifying Mixture Models Through Function Approximation (2006, methodology): “The resultant, more compact model can then be used efficiently in the learning process or the subsequent testing phase.”
A review of novelty detection (2014, methodology): “This kernel density estimator is often termed the Parzen windows estimator [143].”