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 Amendment
This Office Action is in response to applicant’s communication filed 4 May 2026, in response to the Office Action mailed 18 February 2026. The applicant’s remarks and any amendments to the claims or specification have been considered, with the results that follow.
Specification
The lengthy specification has not been checked to the extent necessary to determine the presence of all possible minor errors. Applicant’s cooperation is requested in correcting any errors of which applicant may become aware in the specification.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention.
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.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claim(s) 1, 3-9, 11, 14, 15, and 18-20 is/are rejected under 35 U.S.C. 103 as being unpatentable over Troncoso Pastoriza (EP 3461054 A1), in view of Lam (US 2023/0108963), and further in view of Crockett (US 12,155,746).
As per claim 1, Troncoso Pastoriza teaches a system, comprising a processor [a server including a processing module (fig. 1; etc.)] to:
receive a ciphertext comprising a fully homomorphic encrypted (FHE) time series from a client device [a server receives “somewhat practical fully homomorphic” encrypted ciphertext from a client device (paras. 0018-22; figs. 1, 3A; etc.); which is fully homomorphic encrypted (FHE) time series data];
train an ARIMA model on the ciphertext using an estimated error and approximating polynomials [an Auto-Regressive Integrated Moving Average (ARIMA) model (para. 0025, etc.) is trained on multiple training datasets and used for predictions (paras. 0020, 0086-91; etc.) using estimated residual scores (error) (paras. 0089-95, etc.) and iteratively approximating polynomials (paras. 0036, 0078-81, etc.)]; and
generate an encrypted model and send the encrypted model to the client device [The method also comprises the second entity (server) computing an encrypted model for prediction; computing an encrypted prediction result for the input data using the encrypted model for prediction and the encrypted input data; and transmitting the encrypted prediction result to the first entity (client) (paras. 0012-15, etc.) and can include sharing the encrypted model with the client device via an interactive protocol (para. 0026, etc.)].
While Troncoso Pastoriza teaches that the process estimates the error for training the ARIMA model (see above), it has not been relied upon for teaching [estimating] an error for training [the] autoregressive integrated moving average (ARIMA) model using a partial subset of recent values of the FHE time series selected to limit homomorphic multiplication depth.
Lam teaches [estimating] the error for training the ARIMA model using a partial subset of recent values of the FHE time series [an ARMA model is used to calculate an ARMA regression error based on historical data, using ordinary least squared with respect to first and second subsets of the data (paras. 0015, 0024, 0090, etc.); for training the ARIMA model with recent values of the FHE time series of the system of Troncoso Pastoriza, above].
Troncoso Pastoriza and Lam are analogous art, as they are within the same field of endeavor, namely training and utilizing Auto-Regressive-Moving-Average models to make predictions.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to estimate the error for the ARMA model using partial subsets of recent values, as taught by Lam, to estimate the error for the ARIMA model on subsets of recent values in the ciphertext taught by Troncoso Pastoriza.
Lam provides motivation as [by utilizing subsets of the historical data, the model speed, efficiency and accuracy can be improved (paras. 0006-9, etc.)].
Crockett teaches a partial subset of recent values of the FHE time series selected to limit homomorphic multiplication depth [a homomorphic circuit of a logistic regression training function may comprise a series of homomorphic gates that accepts a ciphertext of an input … where the multiplicative depth of a homomorphic circuit is reduced by identifying a first portion of homomorphic operations from a first loop iteration that can be performed in parallel with a second portion of homomorphic operations from a subsequent loop iteration (col 2, line 60 to col. 3, line 12; etc.), for selecting the subset(s) of the FHE time series in Troncoso Pastoriza/Lam, above].
Troncoso Pastoriza/Lam and Crockett are analogous art, as they are within the same field of endeavor, namely optimizing a regressive model utilizing homomorphic operations.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to select subsets of data/operations from different times/iterations, as taught by Crockett, in the selection of the subsets of the recent values of the FHE time series for estimating the error of the ARIMA model in the system taught by Troncoso Pastoriza/Lam.
Crockett provides motivation as [In at least some embodiments, the efficiency of the evaluation depends on the structure of function F( ), and in particular, its multiplicative depth, which refers to the maximum number of consecutive multiplications required to evaluate F( ). Homomorphic encryption can be used in a variety of settings—for example, a HE-based can be used by multiple institutions to share data in an encrypted format and run machine learning algorithms on the encrypted data without decrypting. With an HE-based approach, encrypted data for training a machine learning algorithm can be delegated to any party—even an untrusted third party—without revealing the underlying contents of the training data (col. 2, lines 25-37; etc.)].
As per claim 3, Troncoso Pastoriza/Lam/Crockett teaches wherein the processor is to estimate the error during training using a plurality of partial subsets of recent values in the ciphertext [the ARMA model is used to calculate an ARMA regression error based on historical data, using ordinary least squared with respect to first and second subsets of the data (Lam: paras. 0015, 0024, 0090, etc.) with somewhat practical fully homomorphic” encrypted ciphertext from a client device (Troncoso Pastoriza: paras. 0018-22; figs. 1, 3A; etc.)], send the client device a plurality of associated encrypted predictions [The method also comprises the second entity (server) computing an encrypted model for prediction; computing an encrypted prediction result for the input data using the encrypted model for prediction and the encrypted input data; and transmitting the encrypted prediction result to the first entity (client) (Troncoso Pastoriza: paras. 0012-15, etc.)], and receive a selected partial subset of the plurality of partial subsets to use for training the ARIMA model [the ARMA model is used to calculate an ARMA regression error based on historical data, using ordinary least squared with respect to first and second subsets of the data (Lam: paras. 0015, 0024, 0090, etc.)].
As per claim 4, Troncoso Pastoriza/Lam/Crockett teaches wherein the encrypted model comprises encrypted parameters for the ARIMA model [the encrypted model includes encrypted model parameters (of the ARIMA model) (Troncoso Pastoriza: para. 0026; fig. 6; etc.)].
As per claim 5, Troncoso Pastoriza/Lam/Crockett teaches wherein the processor is to compute a predetermined number of differences based on a difference parameter of the ARIMA model [the homomorphic ARIMA model includes differencing, which determines a number of differences recursively, as many times as a specified d value (difference parameter) (Troncoso Pastoriza: paras. 0158-160, etc.)].
As per claim 6, Troncoso Pastoriza/Lam/Crockett teaches wherein the ARIMA model comprises a moving average (MA) order having a value of one [the ARIMA model includes a moving average MA(q) process where ϕ(z) = 1 (the MA order has a value of one) (Troncoso Pastoriza: para. 0133, etc.)].
As per claim 7, Troncoso Pastoriza/Lam/Crockett teaches wherein the ciphertext is encrypted under fully homomorphic encryption, and the ARIMA model is trained and the encrypted model generated under fully homomorphic encryption [the ciphertext is “somewhat practical fully homomorphic” encrypted (Troncoso Pastoriza: paras. 0018-22, etc.) and sent to the server to train the ARIMA model (Troncoso Pastoriza: paras. 0086-88; figs. 5-6; etc.)].
As per claim 8, Troncoso Pastoriza teaches a computer-implemented method, comprising:
receiving, via a processor, a fully homomorphic encryption (FHE) encrypted time series [a server receives “somewhat practical fully homomorphic” encrypted ciphertext from a client device (paras. 0018-22; figs. 1, 3A; etc.); which is fully homomorphic encrypted (FHE) time series data];
computing, under FHE, a predetermined number of differences based on a difference parameter of an autoregressive integrated moving average (ARIMA) model to be used to model the FHE encrypted time series [the homomorphic ARIMA model includes differencing, which determines a number of differences recursively, as many times as a specified d value (difference parameter) (paras. 0158-160, etc.)];
computing, under FHE, model parameters of the ARIMA model using approximating polynomials [an Auto-Regressive Integrated Moving Average (ARIMA) model (para. 0025, etc.) is trained on multiple training datasets and used for predictions (paras. 0020, 0086-91; etc.) using iteratively approximated polynomials (paras. 0036, 0078-81, etc.)]; and
outputting, via the processor, a trained model comprising the computed model parameters [The method also comprises the second entity (server) computing an encrypted model for prediction; computing an encrypted prediction result for the input data using the encrypted model for prediction and the encrypted input data; and transmitting the encrypted prediction result to the first entity (client) (paras. 0012-15, etc.) and can include sharing the encrypted model with the client device via an interactive protocol (para. 0026, etc.)].
While Troncoso Pastoriza teaches that the process estimates the error for training the ARIMA model (see above), it has not been relied upon for teaching [estimating], under FHE, an error for the ARIMA model using a partial subset of recent values of the FHE time series selected to limit homomorphic multiplication depth.
Lam teaches [estimating], under FHE, an error for the ARIMA model using a partial subset of recent values of the FHE time series [an ARMA model is used to calculate an ARMA regression error based on historical data, using ordinary least squared with respect to first and second subsets of the data (paras. 0015, 0024, 0090, etc.); for training the ARIMA model with recent values of the FHE time series of the system of Troncoso Pastoriza, above].
Troncoso Pastoriza and Lam are analogous art, as they are within the same field of endeavor, namely training and utilizing Auto-Regressive-Moving-Average models to make predictions.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to estimate the error for the ARMA model using partial subsets of recent values, as taught by Lam, to estimate the error for the ARIMA model on subsets of recent values in the ciphertext taught by Troncoso Pastoriza.
Lam provides motivation as [by utilizing subsets of the historical data, the model speed, efficiency and accuracy can be improved (paras. 0006-9, etc.)].
Crockett teaches a partial subset of recent values of the FHE time series selected to limit homomorphic multiplication depth [a homomorphic circuit of a logistic regression training function may comprise a series of homomorphic gates that accepts a ciphertext of an input … where the multiplicative depth of a homomorphic circuit is reduced by identifying a first portion of homomorphic operations from a first loop iteration that can be performed in parallel with a second portion of homomorphic operations from a subsequent loop iteration (col 2, line 60 to col. 3, line 12; etc.), for selecting the subset(s) of the FHE time series in Troncoso Pastoriza/Lam, above].
Troncoso Pastoriza/Lam and Crockett are analogous art, as they are within the same field of endeavor, namely optimizing a regressive model utilizing homomorphic operations.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to select subsets of data/operations from different times/iterations, as taught by Crockett, in the selection of the subsets of the recent values of the FHE time series for estimating the error of the ARIMA model in the system taught by Troncoso Pastoriza/Lam.
Crockett provides motivation as [In at least some embodiments, the efficiency of the evaluation depends on the structure of function F( ), and in particular, its multiplicative depth, which refers to the maximum number of consecutive multiplications required to evaluate F( ). Homomorphic encryption can be used in a variety of settings—for example, a HE-based can be used by multiple institutions to share data in an encrypted format and run machine learning algorithms on the encrypted data without decrypting. With an HE-based approach, encrypted data for training a machine learning algorithm can be delegated to any party—even an untrusted third party—without revealing the underlying contents of the training data (col. 2, lines 25-37; etc.)].
As per claim 9, Troncoso Pastoriza/Lam/Crockett teaches predicting, via the processor, a future prediction value for the FHE encrypted time series using the estimated error [estimated residual scores (error) are computed (Troncoso Pastoriza: paras. 0089-95, etc.) and the method also comprises the second entity (server) computing an encrypted model for prediction; computing an encrypted prediction result for the input data using the encrypted model for prediction and the encrypted input data; and transmitting the encrypted prediction result to the first entity (client) (Troncoso Pastoriza: paras. 0012-15, etc.)].
As per claim 11, see the rejection of claim 3, above.
As per claim 14, Troncoso Pastoriza/Lam/Crockett teaches wherein computing the model parameters comprises computing, under FHE, a covariance of time series values with corresponding values one entry into the past in the FHE encrypted time series [the computation of the ARIMA model includes calculation of the autocovariance matrix of the time series of n values (which includes corresponding values one entry into the past) (Troncoso Pastoriza: paras. 0134, 0143-146, etc.)].
As per claim 15, Troncoso Pastoriza teaches wherein computing the model parameters comprises constructing a plurality of equations with a plurality of unknowns using computed variance and covariance values, and solving a set of equations under FHE to compute a phi parameter of the ARIMA model [In order to do this, we first obtain φ (phi parameter) from the last q equations (Troncoso Pastoriza: para. 0153, etc.), which include computed variance and covariance values (Troncoso Pastoriza: paras. 0148-151, etc.)].
As per claim 18, Troncoso Pastoriza/Lam/Crockett teaches wherein computing the model parameters comprises computing, under FHE, an expected prediction error using a computed variance of the FHE encrypted time series, a covariance of the FHE encrypted time series, and a computed theta value for the ARIMA model [the estimated residuals (prediction error) can be calculated (paras. 0155-157, etc.) from both φ and θ parameters of the model (Troncoso Pastoriza: paras. 0152-154, etc.) and the variance and covariance of the (FHE encrypted) time series data (Troncoso Pastoriza: paras. 0143-148, etc.)].
As per claim 19, see the rejection of claim 8, above, wherein Troncoso Pastoriza/Lam/Crockett also teaches a computer program produce for, the computer program product comprising a computer-readable storage medium having program code embodied therewith, the program code executable by a processor to cause the processor to: [perform the method] [the method may be implemented in cloud-bases software (Troncoso Pastoriza: para. 0031, etc.); which is a computer program stored in a computer-readable storage medium and executed by at least one processor].
As per claim 20, see the rejection of claim 9, above.
Claim(s) 12, 13, and 16 is/are rejected under 35 U.S.C. 103 as being unpatentable over Troncoso Pastoriza, Lam, and Crockett as applied to claim 8 above, and further in view of Brockwell et al. (Introduction to Time Series and Forecasting, Second Edition, 2002, pgs. 0-434).
As per claim 12, Troncoso Pastoriza/Lam/Crockett teaches the computer-implemented method of claim 8, as described above.
While Troncoso Pastoriza/Lam/Crockett teaches computing model parameters (see above) as well as using a set mean of the time series data (see, e.g., Troncoso Pastoriza: paras. 0147-149, for zero-mean series), it has not been relied upon for teaching wherein computing the model parameters comprises computing a mean of the FHE encrypted time series under FHE.
Brockwell teaches wherein computing the model parameters comprises computing a mean of the FHE encrypted time series under FHE [the mean (μ), autocovariance, and variance are calculated from samples of the time series data (pgs. 58-59, section 2.4.1; etc.), for the FHE encrypted time series of Troncoso Pastoriza, above].
Troncoso Pastoriza/Lam/Crockett and Brockwell are analogous art, as they are within the same field of endeavor, namely training and utilizing ARIMA models for time series predictions.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to include computing the mean of the time series data in computing model parameters of the ARIMA model, as taught by Brockwell, for computing the model parameters of the ARIMA model from the FHE encrypted time series data in the system taught by Troncoso Pastoriza/Lam/Crockett.
Troncoso Pastoriza provides motivation as [according to another embodiment where an Auto-Regressive Integrated Moving Average (ARIMA) model [17] is used, encryptions of the corresponding ARIMA coefficients are computed; in these scenarios several models can be calculated depending on the number of variables which are taken into account (para. 0025), For more details on ARIMA models, we refer to [17] (para. 0133), it can be computed more efficiently by resorting to the Levinson-Durbin recursion (see [17]) (para. 0145) and we first obtain φ from the last q equations, and afterwards, θ can be easily derived (for more details see [17]) (para. 0153); where [17] refers to Brockwell (see pg. 4, lines 20-21 for [17])].
As per claim 13, Troncoso Pastoriza/Lam/Crockett/Brockwell teaches wherein computing the model parameters comprises computing a variance of the FHE encrypted time series under FHE based on the computed mean [the variance of the time series can be computed based on the computed mean (Brockwell: pg. 59, section 2.4.1; etc.) for the FHE ciphertext time series data received from a client device (Troncoso Pastoriza: paras. 0018-22; figs. 1, 3A; etc.)].
As per claim 16, Troncoso Pastoriza/Lam/Crockett/Brockwell teaches wherein computing the model parameters comprises computing a mu parameter of the ARIMA model using a mean of the FHE encrypted time series and a computed phi parameter [the mean (μ), autocovariance, and variance are calculated from samples of the time series data (Brockwell: pgs. 58-59, section 2.4.1; etc.) from which a φ parameter can be calculated using the Yule-Walker equations (Brockwell: pg. 140, 5.1.7; Troncoso Pastoriza: paras. 0143, 0155, etc.) and afterwards, θ can be easily derived (Troncoso Pastoriza: para. 0153; Brockwell: pg. 55, section 2.3; etc.)].
Examiner’s Note: the reasoning and motivation for the combination is provided, above, in the rejection of claim 12.
Claim(s) 17 is/are rejected under 35 U.S.C. 103 as being unpatentable over Troncoso Pastoriza (EP 3461054 A1), in view of Lam (US 2023/0108963), further in view of Crockett (US 12,155,746), further in view of Brockwell et al. (Introduction to Time Series and Forecasting, Second Edition, 2002, pgs. 0-434), and further in view of Gurnani et al. (Forecasting of sales by using fusion of Machine Learning techniques, Feb 2017, pgs. 93-101).
As per claim 17, Troncoso Pastoriza/Lam/Crockett/Brockwell teaches wherein computing the model parameters comprises computing a series as predicted with computed mu and phi parameters, computing variance and covariance of values [the mean (μ), autocovariance, and variance are calculated from samples of the time series data (Brockwell: pgs. 58-59, section 2.4.1; Troncoso Pastoriza: pars. 0143-148; etc.) from which a φ parameter can be calculated using the Yule-Walker equations (Brockwell: pg. 140, 5.1.7; Troncoso Pastoriza: paras. 0143, 0155, etc.)], and computing a theta parameters for the ARIMA model using the computed covariance values [the mean (μ), autocovariance, and variance are calculated from samples of the time series data (Brockwell: pgs. 58-59, section 2.4.1; etc.) from which a φ parameter can be calculated using the Yule-Walker equations (Brockwell: pg. 140, 5.1.7; Troncoso Pastoriza: paras. 0143, 0155, etc.) and afterwards, θ can be easily derived (Troncoso Pastoriza: para. 0153; Brockwell: pg. 55, section 2.3; etc.)].
Examiner’s Note: the reasoning and motivation for the combination of Troncoso Pastoriza and Brockwell is provided in the rejection of claim 12, above.
While Troncoso Pastoriza/Lam/Crockett/Brockwell teaches computing the model parameters (see above), it has not been relied upon for teaching wherein computing the model parameters comprises computing a residue series comprising residues of the FHE encrypted time series, and computing values of the residue series.
Gurnani teaches computing a residue series comprising residues of the FHE encrypted time series, and computing values of the residue series [linear models are not able to capture nonlinear patterns accurately, hence to improve the prediction result, their residue (which contains nonlinear pattern) is forecasted by nonlinear ARIMA (pg. 95, section II.B; etc.)].
Troncoso Pastoriza/Lam/Crockett/Brockwell and Gurnani are analogous art, as they are within the same field of endeavor, namely training and utilizing ARIMA models for predictions.
It would have been obvious to one of ordinary skill in the art, before the effective filing date of the claimed invention, to compute the residue series of the data with the ARIMA model, as taught by Gurnani, for the computing of the ARIMA model parameters in the system taught by Troncoso Pastoriza/Lam/Crockett/Brockwell.
Gurnani provides motivation as [Residue obtained by ARIMA is applied to nonlinear models like Neural Network, XGBoost and SVM to obtain forecast of nonlinear patterns missed by ARIMA (pg. 95, section II.B; etc.)].
Response to Arguments
The objections to claims 17 and 19 have been withdrawn due to the amendments filed.
The rejection of claims 19-20 under 35 U.S.C. 101 has been withdrawn due to the amendments filed.
Applicant’s arguments, see the remarks, filed 4 May 2026, with respect to the rejection(s) of claim(s) 1-20 under 35 U.S.C. 102 and/or 103 have been fully considered and are persuasive. Therefore, the rejection has been withdrawn. However, upon further consideration, a new ground(s) of rejection is made in view of Crockett, which has been relied upon for teaching selecting the subset of recent values of the FHE time series to limit homomorphic multiplication depth (see above).
Conclusion
The following is a summary of the treatment and status of all claims in the application as recommended by M.P.E.P. 707.07(i): claims 2 and 10 are cancelled; claims 1, 3-9, and 11-20 are rejected.
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Ruiz (US 2018/0089577 and US 2016/0203413) – disclose forecasting systems utilizing approximation of polynomials and error estimation.
Huang (US 11,295,224) – discloses a system/method for metric prediction using dynamic confidence, including a moving window (subset) of the history of prediction error values.
The examiner requests, in response to this Office action, that support be shown for language added to any original claims on amendment and any new claims. That is, indicate support for newly added claim language by specifically pointing to page(s) and line number(s) in the specification and/or drawing figure(s). This will assist the examiner in prosecuting the application.
When responding to this office action, Applicant is advised to clearly point out the patentable novelty which he or she thinks the claims present, in view of the state of the art disclosed by the references cited or the objections made. He or she must also show how the amendments avoid such references or objections. See 37 CFR 1.111(c).
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 GEORGE GIROUX whose telephone number is (571)272-9769. The examiner can normally be reached M-F 10am-6pm.
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/GEORGE GIROUX/Primary Examiner, Art Unit 2128
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