DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Response to Arguments
Applicant's arguments filed 03/30/2026 have been fully considered but they are not fully persuasive.
Regarding the 101 rejections, applicant’s arguments and amendments to the independent claims are persuasive and overcome the previous 101 rejections. Specifically, applicant’s amended limitations of training, by the computing device, polynomial chaos expansions as a surrogate model to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions, wherein coefficients of the polynomial chaos expansion are learned from a distribution representation of the high dimensional dataset from the set of distributions using a maximum mean discrepancy as a kernel regression loss provides a technical improvement and a practical application because a polynomial chaos expansion surrogate model trained with maximum mean discrepancy improves the efficiency of performing uncertainty quantification with expensive high dimensional data. See pg. 10 of “Remarks”: “The problem is traditional uncertainty quantification techniques are computationally intensive and become prohibitively expensive for high-dimensional data. Paragraph 0006 of the Specification. For example, traditional use of polynomial chaos expansion results in too many coefficients when dealing with high dimensional data. See Paragraph 0066 of the Specification. One practical example of this problem relates to computer vision with video feeds. Video feeds are considered high-dimensional data. As disclosed in paragraph 0092 of the Specification, there is some uncertainty regarding the presence of an object in a video feed because the object is partially hidden. A computer controlling a vehicle needs to be able to deal with the uncertainty regarding the partially hidden object in the video feed to decide whether to avoid the partially hidden object. To solve this technical problem, paragraphs 0050-0051 of the Specification disclose using variational autoencoders (VAEs) for dimensionality reduction and a polynomial chaos expansions (PCEs) as a surrogate model. The VAEs reduce the dimensionality of the high dimensional data so that PCEs can represent the uncertainty in the data. The PCEs are then trained using maximum means discrepancy (MMD) as a kernel regression loss to learn the coefficients of the PCEs. See Paragraphs 0052 and 0080 of the Specification. Once trained, the PCE then can represent the uncertainty shown in the high-dimensional data. Paragraph 0082 of the Specification. The practical application of this is that with the uncertainty mapped out, the previously discussed vehicle can now be steered by a computer to avoid hitting the partially hidden objects.” Applicant’s amendments and corresponding arguments that the claimed invention provides a technical improvement to the field of uncertainty quantification are persuasive. Therefore, the 101 rejections are withdrawn.
Regarding the 103 rejections, applicant's arguments filed with respect to the prior art rejections have been fully considered but they are moot. Applicant has amended the claims to recite new combinations of limitations. Applicant's arguments are directed at the amendment. Please see below for new grounds of rejection, necessitated by Amendment.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1-2, 4, 7-11, 13, and 16-19 are rejected under 35 U.S.C. 103 as being unpatentable over Bohm, et al., Non-Patent Literature “Uncertainty Quantification with Generative Models” (“Bohm”) in view of Schobi, et al., Non-Patent Literature “Polynomial-Chaos-based Kriging” (“Schobi”) and further in view of Ghosh, et al., US Pre-Grant Publication 2018/0341876A1 (“Ghosh”) and Gretton, et al., Non-Patent Literature “A Kernel Two-Sample Test” (“Gretton”).
Regarding claim 1, Bohm discloses:
A method of mapping high dimensional input data to a low dimensional latent representation to determine data uncertainty, (Bohm, pg. 1, “While it is usually tractable to find the maximum of the posterior, i.e. the most probable underlying realization, a full uncertainty quantification [to determine data uncertainty,] of the reconstruction is usually prohibitively expensive. We propose to address these challenges with generative models, which provide a mapping from points in a typically lower dimensional latent space to points in the high dimensional data space [A method of mapping high dimensional input data to a low dimensional latent representation].”).
comprising: receiving…a high dimensional data input and a corresponding data output; (Bohm, pg. 1, “VAEs are designed to model the distribution pφ(x) of high-dimensional input data [comprising: receiving…a high dimensional data input], x, by introducing a mapping pφ(x|z) to a lower dimensional latent representation, z. The latent space variables are enforced to follow a given prior distribution, p(z), which is typically chosen to be a standard normal distribution…The prior distribution, p(z), reflects the distribution of the training data [and a corresponding data output;].”).
training…a variational autoencoder (VAE) with the high dimensional data input to learn a low dimensional latent space representation of the high dimensional data input, (Bohm, pg. 1, “VAEs are designed to model the distribution pφ(x) of high-dimensional input data, x, by introducing a mapping pφ(x|z) to a lower dimensional latent representation, z [training…a variational autoencoder (VAE) with the high dimensional data input to learn a low dimensional latent space representation of the high dimensional data input,].”).
an encoder part of the VAE outputting a set of distributions of the high dimensional dataset in a latent space; (Bohm, pg. 1, “VAEs are designed to model the distribution pφ(x) of high-dimensional input data, x, by introducing a mapping pφ(x|z) to a lower dimensional latent representation, z. The latent space variables are enforced to follow a given prior distribution, p(z), which is typically chosen to be a standard normal distribution; mapping the high dimension data to a lower representation is interpreted as the encoder part of the VAE outputting distributions of the high dimensional data (i.e. an encoder part of the VAE outputting a set of distributions of the high dimensional dataset in a latent space;).”).
sampling…new data samples in the latent space using the set of distributions outputs from the encoder part of the VAE; (Bohm, pg. 1, “The representation of the posterior in the lower dimensional latent space enables tractable posterior analysis. In particular it allows to examine and fit the posterior distribution and draw samples from it [sampling…new data samples in the latent space using the set of distributions outputs from the encoder part of the VAE;].”).
While Bohm teaches a system that determines uncertainty quantification of a low latent distribution of high dimensional data using a VAE, Bohm does not explicitly teach:
…by a computing device…
and training…polynomial chaos expansions as a surrogate model to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions wherein coefficients of the polynomial chaos expansion are learned from a distribution representation of the high dimensional dataset from the set of distributions using a maximum mean discrepancy as a kernel regression loss.
Schobi teaches:
and training…polynomial chaos expansions as a surrogate model to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation (Schobi, pg. 3, “Polynomial chaos expansions (PCE) [and training…polynomial chaos expansions], also know as spectral expansions, approximate the computational model by a series of multivariate polynomials which are orthogonal with respect to the distributions of the input random variables [to map the new data samples in the latent space to the corresponding data output to learn the set of distributions and their relation].”, and Schobi, abstract, “PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables [as a surrogate model].”).
to perform estimation with high-dimensional dataset under uncertainty such as missing values by estimating the values using the set of distributions (Schobi, pg. 2, “Some others may have a unique value which is however not directly measurable and prone to lack of knowledge (epistemic uncertainty). In a probabilistic setup these parameters are modelled by random variables with prescribed joint probability density function, or more generally, by random fields. The goal of uncertainty propagation is to assess the effect of the input uncertainty onto the model output [such as missing values by estimating the values], and consequently onto the performance of the system under consideration…To circumvent this problem, surrogate models may be used, which replace the original computational model by an easy-to-evaluate function (Storlie et al., 2009; Hastie et al., 2001; Forrester et al., 2008). These surrogate models, also known as response surfaces or meta-models, are capable of quickly predicting responses to new input realizations [to perform estimation with high-dimensional dataset under uncertainty].”, and Schobi, pg. 3, “Polynomial chaos expansions (PCE), also know as spectral expansions, approximate the computational model by a series of multivariate polynomials which are orthogonal with respect to the distributions of the input random variables [using the set of distributions].”).
where coefficients of the polynomial chaos expansion are learned from a distribution representation of the high dimensional dataset from the set of distributions… (Schobi, abstract, “PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. A least-square minimization technique may be used to determine the coefficients of the PCE [wherein coefficients of the polynomial chaos expansion are learned from a distribution representation of the high dimensional dataset from the set of distributions…].”).
Bohm and Schobi are both in the same field of endeavor (i.e. uncertainty quantification). It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm and Schobi to teach the above limitation(s). The motivation for doing so is that using PCE improves uncertainty quantification by determining global behavior of a model (cf. Schobi, abstract, “A sparse set of orthonormal polynomials (PCE) approximates the global behavior of the computational model”).
While Bohm in view of Schobi teaches a system that determines uncertainty quantification of a low latent distribution of high dimensional data using a VAE and PCE, the combination does not explicitly teach:
…by a computing device…
…using a maximum mean discrepancy as a kernel regression loss.
Ghosh teaches …by a computing device… (Ghosh, ⁋57, “Computer device 905 in computing environment 900 can include one or more processing units, cores, or processors 910, memory 915 (e.g., RAM, ROM, and/or the like), internal storage 920 (e.g., magnetic, optical, solid state storage, and/or organic), and/or I/O interface 925, any of which can be coupled on a communication mechanism or bus 930 for communicating information or embedded in the computer device 905 […by a computing device…].”).
Bohm, in view of Schobi, and Ghosh are both in the same field of endeavor (i.e. uncertainty quantification). Bohm, in view of Schobi, teaches a base method for uncertainty quantification using a machine learning model. Ghosh teaches a known technique of using a computer to perform machine learning functions. It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, in view of Schobi, and Ghosh to teach the above limitation(s). The motivation for doing so is that applying Ghosh’s known technique of using a computer to perform machine learning to Bohm, in view of Schobi,’s base system of uncertainty quantification would yield predictable results.
While Bohm in view of Schobi and Ghosh teaches a system that learns coefficients for PCE, the combination does not explicitly teach:
…using a maximum mean discrepancy as a kernel regression loss.
Gretton teaches …using a maximum mean discrepancy as a kernel regression loss. (Gretton, abstract, “We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD) […using a maximum mean discrepancy as a kernel regression loss.].”).
Bohm, in view of Schobi and Ghosh, and Gretton are both in the same field of endeavor (i.e. sample comparison). It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, in view of Schobi and Ghosh, and Gretton to teach the above limitation(s). The motivation for doing so is that MMD improves a model’s ability to determine whether samples are related (cf. Gretton, pg. 724, “We address the problem of comparing samples from two probability distributions, by proposing statistical tests of the null hypothesis that these distributions are equal against the alternative hypothesis that these distributions are different (this is called the two-sample problem). Such tests have application in a variety of areas.”).
Regarding claim 2, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Schobi further teaches wherein the polynomial chaos expansion approximates a global behavior of the low dimensional latent space representation using a set of orthogonal polynomials. (Schobi, pg. 3, “Polynomial chaos expansions (PCE), also know as spectral expansions, approximate the computational model by a series of multivariate polynomials which are orthogonal with respect to the distributions of the input random variables [wherein the polynomial chaos expansion approximates a global behavior of the low dimensional latent space representation using a set of orthogonal polynomials.].”).
It would have been obvious to one of ordinary skill in the art before the effective filling date of the present application to combine the teachings of Schobi with the teachings of Bohm and Ghosh for the same reasons disclosed in claim 1.
Regarding claim 4, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Schobi further teaches wherein the coefficients of the polynomial chaos expansion are learned by regression fitting comprising minimizing a loss function. (Schobi, abstract, “PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. A least-square minimization technique may be used to determine the coefficients of the PCE [wherein the coefficients of the polynomial chaos expansion are learned by regression fitting comprising minimizing a loss function.].”).
It would have been obvious to one of ordinary skill in the art before the effective filling date of the present application to combine the teachings of Schobi with the teachings of Bohm, Ghosh, and Gretton for the same reasons disclosed in claim 1.
Regarding claim 7, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Bohm further teaches wherein a distribution of the data input into the low dimensional latent space representation and a distribution of the data output from the low dimensional latent space representation are unknown a-priori. (Bohm, pg. 1, “VAEs are designed to model the distribution pφ(x) of high-dimensional input data, x, by introducing a mapping pφ(x|z) to a lower dimensional latent representation, z. The latent space variables are enforced to follow a given prior distribution, p(z), which is typically chosen to be a standard normal distribution; a VAE is a unsupervised model and thus the low dimensional representation is determined during learning and not known before (i.e. wherein a distribution of the data input into the low dimensional latent space representation and a distribution of the data output from the low dimensional latent space representation are unknown a-priori.).”).
Regarding claim 8, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Bohm further teaches wherein said sampling step comprises sampling only the latent space without any prior statistical assumptions on the data output from the low dimensional latent space representation. (Bohm, pg. 1, “Given a generative model, the posterior of the latent variables for a given data realization can be modeled with Bayes rule pφ(z|x) ∝ pφ(x|z)p(z). (1) This formulation allows to address both aforementioned problems: 1) The prior distribution, p(z), reflects the distribution of the training data. 2) The representation of the posterior in the lower dimensional latent space enables tractable posterior analysis. In particular it allows to examine and fit the posterior distribution and draw samples from it; VAE is an unsupervised model therefore the low dimensional representation is learned during training without prior labels (i.e. wherein said sampling step comprises sampling only the latent space without any prior statistical assumptions on the data output from the low dimensional latent space representation.).”).
Regarding claim 9, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Bohm further teaches wherein the variational autoencoder comprises a neural network based encoder and a neural network based decoder that are jointly optimized in order to maximize an evidence lower bound. (Bohm, pg. 2, “Here, we use a vanilla VAE with mean-field Gaussian posterior and train it under the Evidence Lower BOund (ELBO) (Kingma & Welling, 2013); one of ordinary skill would know that a VAE is comprised of an encoder and decoder neural networks (i.e. wherein the variational autoencoder comprises a neural network based encoder and a neural network based decoder that are jointly optimized in order to maximize an evidence lower bound.).”).
Regarding claim 10, the claim is similar to claim 1 and is rejected under the same rationales. Ghosh teaches the additional limitations of the computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computing device to cause the computing device to perform a method comprising: (Ghosh, ⁋63, “Computer device 905 can be used to implement techniques, methods, applications, processes, or computer-executable instructions in some example computing environments. Computer-executable instructions can be retrieved from transitory media, and stored on and retrieved from non-transitory media [the computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computing device to cause the computing device to perform a method comprising:].”).
Bohm, in view of Schobi and Gretton, and Ghosh are both in the same field of endeavor (i.e. uncertainty quantification). Bohm, in view of Schobi and Gretton, teaches a base method for uncertainty quantification using a machine learning model. Ghosh teaches a known technique of using a computer to perform machine learning functions. It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, in view of Schobi and Gretton, and Ghosh to teach the above limitation(s). The motivation for doing so is that applying Ghosh’s known technique of using a computer to perform machine learning to Bohm, in view of Schobi and Gretton,’s base system of uncertainty quantification would yield predictable results.
Regarding claims 11, 13, and 16-18, the claims are similar to claims 2, 4, and 7-9 and are rejected under the same rationales.
Regarding claim 19, the claim is similar to claim 1 and is rejected under the same rationales. Ghosh teaches the additional limitations of A computer processing system… comprising: a memory device for storing program code; and a hardware processor operatively coupled to the memory device for running the program code to: (Ghosh, ⁋57, “Computer device 905 in computing environment 900 can include one or more processing units, cores, or processors 910, memory 915 (e.g., RAM, ROM, and/or the like), internal storage 920 (e.g., magnetic, optical, solid state storage, and/or organic), and/or I/O interface 925, any of which can be coupled on a communication mechanism or bus 930 for communicating information or embedded in the computer device 905 [A computer processing system… comprising: a memory device for storing program code; and a hardware processor operatively coupled to the memory device for running the program code to:].”).
Bohm, in view of Schobi and Gretton, and Ghosh are both in the same field of endeavor (i.e. uncertainty quantification). Bohm, in view of Schobi and Gretton, teaches a base method for uncertainty quantification using a machine learning model. Ghosh teaches a known technique of using a computer to perform machine learning functions. It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, in view of Schobi and Gretton, and Ghosh to teach the above limitation(s). The motivation for doing so is that applying Ghosh’s known technique of using a computer to perform machine learning to Bohm, in view of Schobi and Gretton,’s base system of uncertainty quantification would yield predictable results.
Claims 5-6 and 14-15 are rejected under 35 U.S.C. 103 as being unpatentable over Bohm, et al., Non-Patent Literature “Uncertainty Quantification with Generative Models” (“Bohm”) in view of Schobi, et al., Non-Patent Literature “Polynomial-Chaos-based Kriging” (“Schobi”) and further in view of Ghosh, et al., US Pre-Grant Publication 2018/0341876A1 (“Ghosh”), Gretton, et al., Non-Patent Literature “A Kernel Two-Sample Test” (“Gretton”), and Li, et al., Non-Patent Literature “Generative Moment Matching Networks” (“Li”).
Regarding claim 5, Bohm in view of Schobi, Ghosh, and Gretton teaches the computer-implemented method of claim 1. Bohm further teaches from the low dimensional latent space representation to a model response of the low dimensional latent space representation. (Bohm, pg. 1, “The representation of the posterior in the lower dimensional latent space enables tractable posterior analysis. In particular it allows to examine and fit the posterior distribution and draw samples from it [from the low dimensional latent space representation to a model response of the low dimensional latent space representation.].”).
While the combination teaches a system that learns coefficients using a maximum mean discrepancy, the combination does not explicitly teach wherein the maximum mean discrepancy is used to match high order moments of an output distribution of the data output.
Li teaches wherein the maximum mean discrepancy is used to match high order moments of an output distribution of the data output (Li, pg. 2 col. 1, “Formally, the following MMD [wherein the maximum mean discrepancy] measure computes the mean squared difference of the statistics of the two sets of samples. Taking φ to be the identity function leads to matching the sample mean, and other choices of φ can be used to match higher order moments [is used to match high order moments of an output distribution of the data output].”).
Bohm, in view of Schobi, Ghosh, and Gretton, and Li are both in the same field of endeavor (i.e. generative models). It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, in view of Schobi, Ghosh, and Gretton, and Li to teach the above limitation(s). The motivation for doing so is that matching order moments of an output distribution in MMD improves model learning efficiency (cf. Li, pg. 1 col. 2, “Training a GMMN to minimize this discrepancy can be interpreted as matching all moments of the model distribution to the empirical data distribution. Using the kernel trick, MMD can be represented as a simple loss function that we use as the core training objective for GMMNs. Using minibatch stochastic gradient descent, training can be kept efficient, even with large datasets.”).
Regarding claim 6, Bohm in view of Schobi, Ghosh, Gretton, and Li teaches the computer-implemented method of claim 5. Li further teaches further comprising choosing a Gaussian kernel function to capture the high order moments. (Li, pg. 2 col. 2, “For universal kernels like the Gaussian kernel, defined as k(x, x0 ) = exp(− 1 2σ |x − x 0 | 2 ), where σ is the bandwidth parameter, we can use a Taylor expansion to get an explicit feature map φ that contains an infinite number of terms and covers all orders of statistics [further comprising choosing a Gaussian kernel function to capture the high order moments.].”).
Bohm, Schobi, Ghosh, Gretton and Li are all in the same field of endeavor (i.e. machine learning). It would have been obvious for a person having ordinary skill in the art before the effective filing date of the claimed invention to combine Bohm, Schobi, Ghosh, Gretton and Li to teach the above limitation(s). The motivation for doing so is that using Guassian kernels in MMD improves performance by considering all moments between the distributions (cf. Li, pg. 2 col. 2, “For universal kernels like the Gaussian kernel, defined as k(x, x0 ) = exp(− 1 2σ |x − x 0 | 2 ), where σ is the bandwidth parameter, we can use a Taylor expansion to get an explicit feature map φ that contains an infinite number of terms and covers all orders of statistics. Minimizing MMD under this feature expansion is then equivalent to minimizing a distance between all moments of the two distributions.”).
Regarding claims 14-15, the claims are similar to claims 5-6 and rejected under the same rationales.
Conclusion
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to NICHOLAS S WU whose telephone number is (571)270-0939. The examiner can normally be reached Monday - Friday 8:00 am - 4:00 pm EST.
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/N.S.W./Examiner, Art Unit 2148 /MICHELLE T BECHTOLD/Supervisory Patent Examiner, Art Unit 2148
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