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Building machine learning models with encrypted data

Building machine learning models with encrypted data

Building machine learning models with encrypted data
New approach to homomorphic encryption speeds up the training of encrypted machine learning models sixfold.
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The prevalence and success of machine learning have given rise to services that enable customers to train machine learning models in the cloud. In one scenario, a customer would upload training data to a cloud-based service and receive a trained model in return.
Homomorphic encryption (HE), a technology that allows computation on encrypted data, would give this procedure an extra layer of security. With HE, a customer would upload encrypted training data, and the service would use the encrypted data to directly produce an encrypted machine learning model, which only the customer could then decrypt.
At the 2020 Workshop on Encrypted Computing and Applied Homomorphic Cryptography, we presented a  paper  exploring the application of homomorphic encryption to logistic regression, a statistical model used for myriad machine learning applications, from genomics to tax compliance. Our paper shows how to train logistic-regression models on encrypted data six times as fast as prior work.
Homomorphic encryption
Homomorphic encryption provides an application programming interface (API) for evaluating functions on encrypted data. We refer to a message as m and its encryption as m with a box around it. Two of the operations in this API are the HE versions of addition and multiplication, which we present at right. The inputs are encrypted values, and the output is the encryption of the sum or product of the plaintext values. 
A circuit with a multiplicative depth of three.
The eval operation takes a description of an arbitrary function ƒ as a circuit ƒ-hat (ƒ with a circumflex accent above it) expressed using only the HE versions of addition and multiplication, as in the example at left. Given ƒ-hat and an encrypted input, eval produces an encryption of the output of evaluating ƒ on the input m.
For example, to evaluate ƒ(x) = x4 + 2 on encrypted data, we could use the circuit ƒ1-hat at right. This would be to use ƒ1-hat and the encrypted version of x as the inputs to the eval operation and x4 + 2 as ƒ(m).
Multiplicative depth
A circuit with a multiplicative depth of two.
The efficiency of the eval operation depends on a property called multiplicative depth, the maximum number of multiplications along any path through a circuit. In the example at right, ƒ1-hat has a multiplicative depth of three, since there is a path that contains three multiplications but no path that has more than three multiplications. However, this is not the most efficient circuit for computing ƒ(x) = x4 + 2 .
Consider, instead, the circuit at left. This circuit also computes x4 + 2 but has a multiplicative depth of only two. It is therefore more efficient to evaluate ƒ2-hat than to evaluate ƒ1-hat.
Model training with homomorphic encryption
We can now see how homomorphic encryption could be used to securely outsource the training of a logistic-regression model. Customers would encrypt training data with keys they generate and control and send the encrypted training data to a cloud service. The service would compute an encrypted model based on the encrypted data and send it back to the customer; the model could then be decrypted with the customer’s key.
The most challenging part of deploying this solution is expressing the logistic-regression-model training function as a low-depth circuit. Prior research on encrypted logistic-regression-model training has explored several variations on the logistic-regression training function. For example:
Training on all samples at once versus using minibatches;
Alternatives to classic gradient descent, such as Nesterov’s accelerated gradient;
Training with variations of the fixed-Hessian method.
Previously, the lowest-depth (and therefore most efficient) circuits for logistic-regression training had multiplicative depth 5k, where k is the number of minibatches of data that the model is trained on. 
We revisited one of these existing solutions and created a circuit with multiplicative depth 2.5k for k minibatches — half the multiplicative depth. This effectively doubles the number of minibatches that can be incorporated into the model in the same amount of time.
Techniques
The logistic-regression-training algorithm can be expressed as a sequence of linear-algebra computations. Prior work showed how to evaluate a limited number of linear-algebra expressions on encrypted data when certain conditions apply. Our paper generalizes those results, providing a complete “toolkit” of homomorphic linear-algebra operations, enabling addition and multiplication of scalars, encrypted vectors, and encrypted matrices. The toolkit is generic and can be used with a variety of linear-algebra applications.
We combine the algorithms in the toolkit with well-established compiler techniques to reduce the circuit depth for logistic-regression model training. First, we use loop unrolling, which replaces the body of a loop with two or more copies of itself and adjusts the loop indices accordingly. Loop unrolling enables further optimizations that may not be possible with just a single copy of the loop body.
We also employ pipelining, which allows us to start one iteration of a loop while still working on the previous iteration. Finally, we remove data dependencies by duplicating some computations. This has the effect of increasing the circuit width (the number of operations that can be performed in parallel), while reducing the circuit depth. 
We note that despite the increased circuit width, computing this lower-depth circuit is faster than computing previous circuits even on a single core. If the server has many cores, we can further improve training time, since our wide circuit provides ample opportunity for parallelism.
Results
We compared our circuit for logistic-regression training to an earlier baseline circuit, using the MNIST data set, an image-processing data set consisting of handwritten digits. Both circuits were configured to incorporate six minibatches into the resulting model. In practice, both circuits would have to be applied multiple times to accommodate a realistic number of minibatches. 
Our circuit requires more encrypted inputs than the baseline; with the circuit parameters we chose, that corresponded to about an 80% increase in bandwidth requirements. Even though our circuit involves four times as many multiplications as the baseline, we can evaluate it more than six times as rapidly (13 seconds, compared to 80 seconds for the baseline) using a parallel implementation. Our homomorphically trained model had the same accuracy as a model trained on the plaintext data for the MNIST data set.
Training other model types
Creating efficient homomorphic circuits is a manual, time-consuming process. To make it easier for Amazon Web Services (AWS) and others to create circuits for other functions — such as training functions for other machine learning models — we created the Homomorphic Implementor’s Toolkit (HIT), a C++ library that provides high-level APIs and evaluators for homomorphic circuits. HIT is available today  on GitHub . 
Research areas
Eric Crockett is an applied scientist with Amazon Web Services' Cryptography team.
Related Publications
Eighth Workshop on Encrypted Computing and Applied Homomorphic Cryptography
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Sr. Economist
US, WA, Seattle
Interested in Amazon Alexa and the future of voice-powered connected devices? Interested in working in a high impact role? This is an opportunity to join one of the fastest-growing and most innovative businesses at Amazon. Third-party hardware makers can integrate the Alexa Voice Service (AVS), the brain behind Amazon Echo, into their products. AVS is enabling many new connected devices and exciting consumer use cases in the home and on the go.This role will serve as the lead economics POC supporting the AVS business. As part of this role, you will lead coordination with other economics POCs across the broader Alexa organization, and build out a longer-term roadmap for econ-related initiatives to support key AVS business priorities. You will lead several near-term initiatives with a focus on causal inference, and have opportunity for exposure to a broader set of focus areas over time (e.g. price elasticity).Responsibilities· Identification/measurement/tracking of specific High Value Actions (HVAs) and Negative Value Actions (NVAs) for driving engagement on AVS devices.· Own building, scaling, and managing HVA/NVA models.· Developing data-driven, scientific approaches to measure downstream value of various device interactions.· Developing data-driven, scientific approaches to measure the downstream impact of Alexa engagement on partner KPIs.· Conduct A/B testing to validate model performance.· Quantifying the business impact of product changes and strategic decisions.
Sr. Research Scientist
US, WA, Seattle
Are you passionate about conducting measurement research and experiments to assess and evaluate talent? Would you like to see your research in products that will drive key behaviors at scale to improve the employee experience and raise the bar of talent at Amazon? If so, you should consider joining the Global Talent Management (GTM) Science Organization.Amazon GTM Science is an innovative organization that exists to propel Amazon HR towards being the most scientific HR organization on earth. The GTM Science mission is to use Science to assist and measurably improve every talent decision made at Amazon. We do this by discovering signals in workforce data, deploying statistical models into Amazon’s talent products, and guiding the broader GTM team to pursue high-impact opportunities with tangible returns. This multi-disciplinary approach spans capabilities, including: data engineering, reporting and analytics, research and behavioral sciences, and applied sciences such as economics and machine learning.We are seeking measurement Scientists with deep quantitative expertise developing assessment and validating measures (assessments, performance evaluations, and surveys) to evaluate talent at Amazon. This person will possess knowledge of different measurement approaches to evaluate performance, a strong psychometrics background, scientific survey methodology, validation, adverse impact analysis, and experience developing legally defensible talent evaluation programs. In this role you will:· Lead the global research strategy developing and experimenting on how to evaluate talent· Conduct Psychometrics analyses to evaluate integrity and practical application of different methods· Develop and iterate on testing, experimenting, and evaluating content prior to global launch· Identify research streams to evaluate how to mitigate or remove sources of measurement error· Partner closely and drive effective collaborations across multi-disciplinary research and product teams· Manage full life cycle of large scale research program
Applied Science Manager
US, NY, New York
Amazon Advertising is one of Amazon's fastest growing and most profitable businesses. As a core product offering within our advertising portfolio, Sponsored Products (SP) helps merchants, retail vendors, and brand owners succeed via native advertising, which grows incremental sales of their products sold through Amazon. The SP team's primary goals are to help shoppers discover new products they love, be the most efficient way for advertisers to meet their business objectives, and build a sustainable business that continuously innovates on behalf of customers. Our products and solutions are strategically important to enable our Retail and Marketplace businesses to drive long-term growth. We deliver billions of ad impressions and millions of clicks and break fresh ground in product and technical innovations every day!We're looking for an Applied Science Manager who combines exceptional technical, research, analytical, and innovative capabilities to lead a team that will be integral to delivering products and services for millions of shoppers and hundreds of thousand of advertisers. As an Applied Science Manager, you will be responsible for data-driven improvements and evaluation for our localization models, including text, images, and video localization. You will be responsible for leading a team of applied scientists and ML engineers to build ML models for delivering on state-of-the-art localization while identifying opportunities to leverage ML for beyond localization, including, international expansion and global campaigns. Your work will directly impact our customers in the form of products and services used directly by our advertisers as well as our 3P integrators.Key Responsibilities:· Lead a team of scientists and engineers and oversee development and research projects at various stages ranging from initial exploration to deployment into production systems.· Rapidly design, prototype and test many possible hypotheses in a high-ambiguity environment, making use of both quantitative and business judgment.· Collaborate with software engineering teams to integrate successful experiments into large scale, highly complex production services.· Report results in a scientifically rigorous way.· Interact with software engineers, product managers and related domain experts to dive deep into the types of challenges that we need innovative solutions for.Impact and Career Growth:You will invent new shopper and advertiser experiences, and accelerate the pace of Machine Learning and Optimization.Influence customer facing shopping experiences to helping suppliers grow their retail business and the auction dynamics that leverage native advertising, this role will be powering the engine of one the fastest growing businesses at Amazon.Define a long-term science vision for our ad marketplace, driven fundamentally from the needs of our customers, translating that direction into specific plans for research and applied scientists, as well as engineering and product teams.This is a role that combines science leadership, organizational ability, technical strength, product focus and business understanding.Why you love this opportunity:Amazon is investing heavily in building a world class advertising business and we are responsible for defining and delivering a collection of self-service performance advertising products that drive discovery and sales. Our products are strategically important to our Retail and Marketplace businesses driving long term growth. We deliver billions of ad impressions and millions of clicks daily and are breaking fresh ground to create world-class products. We are highly motivated, collaborative and fun-loving with an entrepreneurial spirit and bias for action. With a broad mandate to experiment and innovate, we are growing at an unprecedented rate with a seemingly endless range of new opportunities.Team video ~ https://youtu.be/zD_6Lzw8raE
Applied Scientist - Amazon Music, New Projects
US, CA, Culver City
Want to build the future of music and audio entertainment?Imagine being part of an agile team, where your ideas have the potential to reach millions. Envision working within a startup atmosphere, while being able to leverage the resources of a Fortune-500 company. Picture working on bleeding-edge consumer-facing products, where every team member is a critical voice in the decision-making process. Welcome to Amazon Music’s New Projects team.Our team builds new experiences for Amazon Music listeners. We help our customers discover up-and-coming creators, while also having access to their favorite music and podcasts. We build systems that are distributed around the world, spanning our music apps, web player, and voice-forward experiences on mobile and Amazon Echo devices, powered by Alexa. Amazon Music products support our mission of delivering audio entertainment in new and exciting ways that listeners love.Amazon Music’s New Projects team is looking for founding team members across a variety of functions, including software engineering/development, product, marketing, design, and more. Come make history, as we launch new projects for millions of listeners.

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