We consider a project (model) owner that would like to train a model by utilizing the local private data and compute power of interested data owners, i.e., trainers. Our goal is to design a data marketplace for such decentralized collaborative/federated learning applications that simultaneously provides i) proof-of-contribution based reward allocation so that the trainers are compensated based on their contributions to the trained model; ii) privacy-preserving decentralized model training by avoiding any data movement from data owners; iii) robustness against malicious parties (e.g., trainers aiming to poison the model); iv) verifiability in the sense that the integrity, i.e., correctness, of all computations in the data market protocol including contribution assessment and outlier detection are verifiable through zero-knowledge proofs; and v) efficient and universal design. We propose a blockchain-based marketplace design to achieve all five objectives mentioned above. In our design, we utilize a distributed storage infrastructure and an aggregator aside from the project owner and the trainers. The aggregator is a processing node that performs certain computations, including assessing trainer contributions, removing outliers, and updating hyper-parameters. We execute the proposed data market through a blockchain smart contract. The deployed smart contract ensures that the project owner cannot evade payment, and honest trainers are rewarded based on their contributions at the end of training. Finally, we implement the building blocks of the proposed data market and demonstrate their applicability in practical scenarios through extensive experiments.

Machine learning is a special type of computer program that can learn and improve on its own by looking at examples or data. Just like how you learn new things by looking at pictures or watching videos, machine learning programs can also learn from pictures or data. For example, imagine you want to teach a computer how to recognize dogs and cats in pictures. You would show the computer lots of pictures of dogs and cats and tell it which ones are dogs and which ones are cats. Then, the computer would start to learn what features make a dog a dog and a cat a cat.

The naive approach: Take the derivative of the loss function which is an average of the losses calculated on every example in the dataset, a full update is powerful but it has some drawbacks… Drawbacks: . Can be extremely slow as we need to pass over the entire dataset to make a single update. . If there is a lot of redundancy in the training data, the benefit of a full update is very low The extreme approach Consider only a single example at a time and update steps based on one observation at a time, does that remind you of something?? Yes, it's the stochastic gradient descent algorithm or SGD. It can be effective even in large datasets but it also has some drawbacks… Drawbacks: . It can take longer to process one sample at a time compared to a full batch .

We've finished the Data Preprocessing part and now it's time to start making Machine Learning Models. We're are going to start with the Simple Linear Regression Model and I will show you how to do it in R. To Learn how to do Simple Linear Regressions in Python, go Here. Before we begin, we need to understand our data and the problem we are trying to solve. I have prepared the dataset that we are going to be using in this tutorial. However, feel free to use any dataset that you may have, and see if you'll get similar results.

Create a regressor and call it, 'poly_reg'. Assign the regressor to the lm() function as we did in linear regression. The function takes two arguments. The formula and the data, same way we did in linear regression. To transform this from a linear regression to a polynomial regression model, we need to add some polynomial features.

We are going to learn how to implement a Multiple Linear Regression model in R. This is a bit more complex than Simple Linear Regression but it's going to be so practical and fun. Multiple Linear Regression is a data science technique that uses several explanatory variables to predict the outcome of a response variable. A Multiple linear regression model attempts to model the relationship between two or more explanatory variables (independent variables) and a response variable (dependent variable), by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y.

Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain observation data with coarse time intervals from fixed-point observations due to experimental costs or measurement constraints. Recently, modeling population dynamics by using continuous normalizing flows (CNFs) and dynamic optimal transport has been proposed to infer the sample trajectories from a fixed-point observed population. While the sample behavior in CNFs is deterministic, the actual sample in biological systems moves in an essentially random yet directional manner. Moreover, when a sample moves from point A to point B in dynamical systems, its trajectory typically follows the principle of least action in which the corresponding action has the smallest possible value. To satisfy these requirements of the sample trajectories, we formulate the Lagrangian Schr\"odinger bridge (LSB) problem and propose to solve it approximately by modeling the advection-diffusion process with regularized neural SDE. We also develop a model architecture that enables faster computation of the loss function. Experimental results show that the proposed method can efficiently approximate the population-level dynamics even for high-dimensional data and that using the prior knowledge introduced by the Lagrangian enables us to estimate the sample-level dynamics with stochastic behavior.

Composite materials with 3D architectures are desirable in a variety of applications for the capability of tailoring their properties to meet multiple functional requirements. By the arrangement of materials' internal components, structure design is of great significance in tuning the properties of the composites. However, most of the composite structures are proposed by empirical designs following existing patterns. Hindered by the complexity of 3D structures, it is hard to extract customized structures with multiple desired properties from large design space. Here we report a multi-objective driven Wasserstein generative adversarial network (MDWGAN) to implement inverse designs of 3D composite structures according to given geometrical, structural and mechanical requirements. Our framework consists a GAN based network which generates 3D composite structures possessing with similar geometrical and structural features to the target dataset. Besides, multiple objectives are introduced to our framework for the control of mechanical property and isotropy of the composites. Real time calculation of the properties in training iterations is achieved by an accurate surrogate model. We constructed a small and concise dataset to illustrate our framework. With multiple objectives combined by their weight, and the 3D-GAN act as a soft constraint, our framework is proved to be capable of tuning the properties of the generated composites in multiple aspects, while keeping the selected features of different kinds of structures. The feasibility on small dataset and potential scalability on objectives of other properties make our work a novel, effective approach to provide fast, experience free composite structure designs for various functional materials.

Abstract--In the setting of federated optimization, where a global model is aggregated periodically, step asynchronism occurs when participants conduct model training by efficiently utilizing their computational resources. It is well acknowledged that step asynchronism leads to objective inconsistency under non-i.i.d. To address this issue, we propose a new algorithm FedaGrac, which calibrates the local direction to a predictive global orientation. Taking advantage of the estimated orientation, we guarantee that the aggregated model does not excessively deviate from the global optimum while fully utilizing the local updates of faster nodes. We theoretically prove that FedaGrac holds an improved order of convergence rate than the state-of-the-art approaches and eliminates the negative effect of step asynchronism. Empirical results show that our algorithm accelerates the training and enhances the final accuracy.

Distributed (or Federated) learning enables users to train machine learning models on their very own devices, while they share only the gradients of their models usually in a differentially private way (utility loss). Although such a strategy provides better privacy guarantees than the traditional centralized approach, it requires users to blindly trust a centralized infrastructure that may also become a bottleneck with the increasing number of users. In this paper, we design and implement P4L: a privacy preserving peer-to-peer learning system for users to participate in an asynchronous, collaborative learning scheme without requiring any sort of infrastructure or relying on differential privacy. Our design uses strong cryptographic primitives to preserve both the confidentiality and utility of the shared gradients, a set of peer-to-peer mechanisms for fault tolerance and user churn, proximity and cross device communications. Extensive simulations under different network settings and ML scenarios for three real-life datasets show that P4L provides competitive performance to baselines, while it is resilient to different poisoning attacks. We implement P4L and experimental results show that the performance overhead and power consumption is minimal (less than 3mAh of discharge).