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Master's in Machine Learning

Online Master of Science in Machine Learning

MSOE’s Master of Science in Machine Learning is an exciting opportunity for working professionals and recent graduates who want to develop advanced skills in machine learning and artificial intelligence (AI) technology. As a distinguished leader in the area of machine learning and applications of AI, MSOE is the ideal choice for you to become a machine learning leader in your own right. Master the skills necessary to develop and deploy machine learning solutions in your technical field.

The online master’s in machine learning program was designed to focus on the application of machine learning to industrial problems, as well as the development and deployment of machine learning-based products, making it unique amongst the current educational offerings in this space. What does that mean for you? Through this program, you will gain skills that can be applied immediately to your current work, boosting your value and leadership abilities well before graduation.

Online Master of Machine Learning Details
  • Offered 100% online
  • Synchronous classes
  • 32 credits to completion
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MSOE and You: Better Together

Earn your master’s or certificate in machine learning online with MSOE. Complete the form to get a program details sheet for the program of your choosing—Master of Science in Machine Learning or Graduate Certificate in Applied Machine Learning—delivered to your inbox.

Machine Learning Master’s Program Outcomes

The machine learning master’s program will prepare you to:

  • Be the lead architect on complex projects involving machine learning and data science
  • Develop solutions that address competing ethical and professional concerns as both technology and society continue to evolve
  • Analyze complex problems involving advanced applications of machine learning and data science and design solutions that meet relevant business, technical and ethical standards
  • Apply a rigorous, scientific approach that includes forming research questions, generating hypotheses, designing and executing experiments and evaluating results to make informed judgments
  • Effectively evaluate and utilize state-of-the-art software and parallel computing hardware in the design and implementation of projects
  • Effectively describe solutions and their implications and communicate results to technical and non-technical audiences
  • Successfully deploy production-quality solutions involving machine learning and data science techniques using current best practices

Real-World Experience, Delivered Directly to You

While there are many post-baccalaureate programs which introduce students to the concepts of machine learning, few, if any, focus on the application of machine learning to industrial problems and the development and deployment of machine learning-based products.

Key features of MSOE’s program include:

  • Depth of technical content
  • Build on prior knowledge with each course to develop deep expertise
  • Industry applications and integration in each course
  • Access to supercomputer ROSIE
  • Small class sizes and synchronous courses
  • Faculty who excel in teaching, research and student support
ROSIE supercomputer at MSOE

Machine Learning Master’s Curriculum

The curriculum for the Master of Science in Machine Learning gets you up to speed on machine learning and AI concepts quickly. In each course, you will go in depth on theory and application of a different essential aspect of machine learning.

Curriculum Overview

Required Courses (28 Credits)

  • CSC 5201—Microservices and Cloud Computing (4 Credits)
  • CSC 5610—AI Tools and Paradigms (4 Credits)
  • CSC 6605—Machine Learning Production Systems (4 Credits)
  • CSC 6621—Applied Machine Learning (4 Credits)
  • CSC 7901—Machine Learning Capstone (4 Credits)
  • MTH 5810—Mathematical Methods for Machine Learning (4 Credits)
  • PHL 6001—AI Ethics and Governance (4 Credits)

Explore the required courses

Electives (4 Credits)

  • CSC 5601—Theory of Machine Learning (4 Credits)
  • CSC 5611—Deep Learning (4 Credits)
  • CSC 5615—Deep Learning in Signal Processing (4 Credits)
  • CSC 5241—GPU Programming (4 Credits)
  • CSC 5980—Topics in Computer Science (Variable Credits)
  • CSC 6999—Computer Science Independent Study (Variable Credits)

Explore the electives

Pathways to Your M.S. in Machine Learning

Start With a Certificate

The M.S. is organized around "stackable" certificates that you can start with or earn along the way:

  • Applied Machine Learning Graduate Certificate (2, 4-credit courses)
  • Machine Learning Engineering Graduate Certificate (2, 4-credit courses)

Attend as a Part-Time Student

If a full-time workload is not ideal, the option to complete the program as a part-time student may help you balance your academic and work commitments. Take one course (4 credits) per semester and complete the program in 4 years.

Five-Year BS to MS Option

Choose from several undergraduate programs that will feed into this master’s program.

Attend as a Full-Time Student

Complete your master’s in as few as 2 years by taking 2 courses (8 credits) per semester.
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Eric Durant
Meet the Master of Science in Machine Learning Program Director
Eric Durant, Ph.D., MBA, P.E.
Office: L-339
Phone: (414) 277-7439
Email: durant@msoe.edu

Dr. Eric Durant is a professor and director of the machine learning program at MSOE. He also served for 16 years as director of MSOE’s computer engineering program. Dr. Durant researches the use of real-time audio processing with a focus on hearing aids, artificial intelligence and deep learning. He also has researched genetic algorithms to efficiently fit audio processing parameters in hearing aids, robust perceptual rank inferencing, beamforming, convex optimization and spatialization. He works regularly with Starkey Hearing Technologies as a senior digital signal processing (DSP) research engineer II and was a visiting professor at NVIDIA.

His areas of expertise include deep learning, audio processing, beamforming, genetic algorithms, convex optimization and hearing aids.
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Admissions

Learn more about the admissions requirements and process to upskill your career with machine learning expertise.
View admissions requirements
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Tuition and Financial Aid

Review the competitive tuition costs and your financial aid opportunities for the machine learning programs.
View tuition and financial aid information
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Online Experience

Learn more about what it’s like to study online with MSOE. Meet the faculty and get a sense of the projects you will take on to grow your machine learning and AI know-how.
Learn More

Machine Learning Master’s Program FAQs

What is a Master of Science in Machine Learning?
The Master of Science in Machine Learning is a 32-credit graduate program that gives you the opportunity to develop advanced skills in machine learning and artificial intelligence (AI) technologies. The master’s program focuses on the application of machine learning to industrial problems and the development and deployment of machine learning-based products.

What is the difference between a master's in AI and machine learning and a graduate certificate in AI and machine learning?
The Graduate Certificate in Applied Machine Learning is an accelerated pathway to learning machine learning and AI technologies and is focused on application to problem solve and move business solutions forward. The M.S. in Machine Learning takes this further by applying theory to the application of AI and machine learning technologies. You will be trained to deploy AI and machine learning tools on products, how to create the systems and the infrastructure for your solutions.

You have the opportunity to apply credits earned in the certificate program toward the master’s program, giving you the flexibility to decide on how you would like to pursue your education in machine learning.

What skills will I gain from the Machine Learning Master's program?
Upon completion of the online Master of Science in Machine Learning, you will be able to:
  • Address competing ethical and professional concerns as you develop machine learning solutions
  • Analyze complex problems involving advanced applications of machine learning and data science
  • Design solutions that meet relevant business, technical and ethical standards
  • Apply a rigorous, scientific approach to make informed judgements—this includes forming research questions, generating hypotheses, designing and executing experiments and evaluating results
  • Evaluate and use state-of-the-art software and parallel computing hardware in the design and implementation of projects
  • Describe solutions and their implications to both technical and non-technical audiences
  • Deploy production-quality solutions that involve best-practice machine learning and data science techniques

What career opportunities are available to MSOE Master's in Machine Learning graduates?
Earning your master’s in machine learning can open the door to leadership opportunities within organizations applying machine learning technologies to drive business solutions. You will be well positioned to function as the lead architect on complex projects involving machine learning and data science. Job titles related to earning this degree include, but are not limited to, artificial intelligence specialist/developer, machine learning engineer, data science specialist, machine learning researcher and machine learning specialist.

Machine learning is taking off globally. Join in and grow your career.

This is an exciting time to build a career working with machine learning and AI technologies. Get the skills you need to lead in this rapidly growing area of technology with MSOE.
Apply Now

Admissions Dates and Deadlines

Jan
17
Application Deadline
January 17
Spring 2025
Jan
21
Start Date
January 21
Spring 2025

Milwaukee School of Engineering has engaged Everspring, a leading provider of education and technology services, to support select aspects of program delivery.

Required Courses

CSC 5201—Microservices and Cloud Computing (4 Credits)

Course Description

This course introduces the concepts, architectural, and practical techniques needed to design and implement cloud-native microservices. Students will design, implement, deploy, and operate a microservice using widely used technologies and current best practices.

Emphasis will be placed on scalable web and machine learning services. Students will apply what they learn in a series of hands-on lab exercises and complete a final project using a distributed computing platform.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Leverage containerization to package and run software
  • Design and implement a basic microservice that interacts through REST APIs, implements access control, uses distributed storage systems, and is deployed in a containerized form
  • Apply access control patterns using authentication and authorization following security best practices
  • Analyze and identify potential throughput, scalability, reliability, and consistency issues with distributed microservice architectures
  • Create and manage continuous integration and deployment to automate software related to microservices and pipelines
  • Deploy a multi-service distributed application using a container orchestration tool

Prerequisites by Topic

  • Version control/Git
  • Operating systems
  • Databases

Course Topics

  • Virtual machines and containers and associated best practices for writing containerized, stateless applications
  • Microservice architectures and implementation patterns including event-driven architectures and designing and implementing REST APIs
  • Distributed storage systems (e.g., key-value stores, columnar stores, object stores, distributed file systems, and relational databases), tradeoffs between consistency, availability, and partition tolerance, and efficient access patterns
  • Continuous integration and deployment technologies and usage patterns
  • Tooling for orchestration and deployment of multi-service systems
  • Software, Function, Platform, and Infrastructure as service paradigms and implementing systems
  • Discussion of public cloud services and comparisons of their offerings

Coordinator: Dr. RJ Nowling

CSC 5610—AI Tools and Paradigms (4 credits)

Course Description

This course introduces topics, tools, languages, and methods used in modern AI practice. Subjects of study include a survey of tools used to perform analysis, data preparation, and visualization along with the algorithms, concepts, and theory underpinning AI. Exercises and assignments will expose students to Jupyter Notebooks and libraries in the Python ecosystem for data science, machine learning, and AI.

Course Learning Outcomes

Upon successful completion of this course, you will be able to:

  • Use a Jupyter notebook environment to write, structure, run, document (with Markdown), and debug Python programs
  • Use Series and Data Frames to load, manipulate, and analyze tabular data sets
  • Leverage appropriate libraries to solve non-trivial data cleaning, preparation, and transformation challenges
  • Employ a plotting library to create simple plots such as histograms, bar or column charts, line plots, and scatter plots including legends, appropriate axis ranges and labels, appropriate font sizes and resolutions
  • Use exploratory data analysis (e.g., summary statistics and visualizations) to characterize data sets and generate hypotheses about the relationships of variables
  • Use a library to train machine learning models and apply models to generate predictions for data
  • Apply and interpret appropriate metrics for evaluating predictions from machine learning models
  • Describe the components of the intelligent agent framework
  • Apply agent and state-based frameworks to solve various problems, such as game playing
  • Provide examples of search problems and techniques for solving them
  • Describe algorithms such as value iteration and q-learning for identifying optimal policies
  • Describe the role of heuristics and describe the trade-offs among completeness, optimality, time complexity, and space complexity
  • Communicate computational results and interpretations in language appropriate for a technical audience
  • Identify ethical implications of potential biases in data sets, algorithms, and applications of AI

Prerequisites by Topic

  • Programming experience

Coordinator: Dr. RJ Nowling

CSC 6605—Machine Learning Production Systems (4 Credits)

Course Description

Students will design, implement, deploy, and operate a machine learning-powered service, including components for data processing, model training, modeling serving, model evaluation, and monitoring. Technologies and design patterns for streaming and batch data processing as well as storage systems will be introduced.

This course builds on and integrates previous course work in offline machine learning and microservices.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Design, implement, deploy, and operate a machine learning-powered RESTful service and supporting backend systems
  • Design and implement data processing systems that use batch and stream processing patterns and technologies for ingesting and processing event data
  • Apply design patterns and data storage systems to design and implement data storage services to support batch and streaming data processing, model training, and model evaluation
  • Create distributed systems to support model training and evaluation
  • Automate and monitor model training, evaluation, deployment, and operation
  • Evaluate and compare architectures of ML-powered Systems

Prerequisites by Topic

  • Cloud computing
  • Micro services
  • Machine learning

Course Topics

  • Distributed batch and streaming data processing platforms and associated programming paradigms
  • Data representation and storage patterns to support batch and streaming data pipelines and services
  • Reliability, consistency, and scalability challenges and solutions for big data systems
  • Patterns for handling model training and evaluation on data that changes or updates over time
  • Tradeoffs between batch and streaming systems in terms of efficiency, computational capabilities, and time until updates are available based on new data
  • Model serving and deployment
  • Monitoring and alerting for services and performance of machine learning model predictions
  • Implementation of systems for common machine learning tasks such as classification/regression and recommendations

Coordinator: Dr. RJ Nowling

CSC 6621—Applied Machine Learning (4 credits)

Course Description

This course introduces concepts of machine learning that explore the study and construction of algorithms that can learn from and make predictions on data.

Topics include conceptual aspects of machine learning, feature engineering, an introduction to deep learning, and applications of machine learning and deep learning. Students will reinforce their learning of machine learning algorithms with hands-on laboratory exercises for development of representative applications.

Course Learning Outcomes

Upon successful completion of this course, you will be able to:

  • Understand the fundamental concepts and application of supervised, unsupervised, semi-supervised, and reinforcement learning
  • Analyze and describe machine learning algorithms including (but not limited to) logistic regression, SVMs, and decision trees
  • Explain the geometric interpretations of linear and non-linear decision boundaries and their relationship to error metrics (e.g., accuracy)
  • Understand the concepts of learning theory, (e.g., what is learnable, bias, variance, overfitting, curse of dimensionality, splitting data for evaluation of model predictions)
  • Estimate and plot decision boundaries described by trained models
  • Interpret coordinate systems and distinguish between feature and parameter spaces
  • Derive, visualize, apply, and interpret metrics and loss functions to assess the quality of model predictions and fit to data
  • Choose and justify appropriate experimental designs (e.g., test-train split, cross-fold validation) for evaluating machine learning models
  • Encode non-numerical variables in tabular data as numerical features
  • Describe implications of feature representations with respect to linear separability
  • Apply approaches for engineering and evaluating new features from existing
  • Describe the fundamentals of deep learning and what is required to be able to use it
  • Compare various modern deep neural network architectures (e.g., convolutional neural networks (CNNs), encoder-decoders, generative adversarial networks (GANs), or transformers).
  • Describe industry examples where deep learning can be used to solve real-world problems

Prerequisites by Topic

  • Software development
  • Python
  • Jupyter Notebooks

Coordinator: Dr. RJ Nowling

CSC 7901—Machine Learning Capstone (4 Credits)

Course Description

Students work on a significant machine learning project that incorporates knowledge from previous course work. Throughout the project students will be supported by a faculty advisor who will meet regularly for project updates and guidance. The capstone concludes with a final report and presentation to faculty and industry representatives.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Integrate and apply knowledge and skills acquired in previous course work
  • Analyze a complex data science problem and apply principles of machine learning to design, implement, and deploy a solution
  • Effectively communicate the design, implementation, and impacts of the solution
  • Identify and address ethical and governance aspects of the problem and solution

Prerequisites by Topic

Machine learning
AI tools

Coordinator: Dr. Derek Riley

MTH 5810—Mathematical Methods for Machine Learning (4 Credits)

Course Description

This course surveys the essential linear algebra and multivariate calculus required for graduate study in machine learning.

Topics include matrix algebra, real vector spaces, inner product spaces, differentiation and Newton’s method, partial differentiation, the gradient, the chain rule, and optimization of multivariate functions.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Describe linear and affine subsets of three-dimensional space both algebraically and geometrically
  • Interpret the value of a dot product geometrically
  • Interpret functions of two variables via the corresponding surface, level curves, and contour plot
  • Perform elementary operations with matrices including manipulating expressions and equations involving matrices
  • Determine if a matrix is invertible and find its inverse in this case
  • Solve systems of linear equations using matrix methods and technology
  • Express the solutions of a consistent matrix equation in parametric vector form
  • Determine if a subset of n-dimensional space is a subspace
  • Find the matrix of a linear transformation and bases for its kernel and range
  • Show that a real number is an eigenvalue of a matrix with real number entries by finding the corresponding eigenvectors
  • Determine the eigenvalues of a matrix using technology
  • Use the inner product to find the length of a vector and the distance between two vectors
  • Determine if a set of vectors is an orthogonal basis for a subspace of R^n
  • Find the projection of a vector onto a subspace of R^n
  • Find a general linear model by solving the normal equation
  • Find and interpret the singular value decomposition of a matrix using technology
  • Use numerical methods to locate extrema of a single-variable function
  • Perform operations with series representations of the single-variable elementary functions
  • Find first and higher-order partial derivatives of a function
  • Interpret partial derivatives as rates of change in applications
  • Find the total differential of a function of more than one variable, use it to estimate change
  • Estimate error propagation using the total differential
  • Construct the matrix form of the multivariate chain rule and use it to find a derivative
  • Find the gradient of a function and interpret its direction
  • Find directional derivatives of a function and interpret the results
  • Determine the maximum, minimum, and saddle points on a surface
  • Interpret mathematics from machine learning literature

Prerequisites by Topic

Single-variable calculus

Course Topics

  • Geometry in three dimensions: lines, planes, distance, surfaces, vectors, and the dot product
  • Matrix algebra
  • Matrix equations and invertibility
  • Real vector spaces
  • Linear transformations and their matrices
  • Inner products, orthogonality, projection, and applications
  • Eigenvectors and eigenvalues and interpretation of matrix factorizations
  • Review of single-variable differentiation
  • Taylor series of elementary functions
  • Finding critical points analytically and numerically
  • Partial derivatives
  • Gradients, directional derivatives, and the Jacobian
  • Extrema of functions of two variables

Coordinator: Dr. Anthony van Groningen

PHL 6001—AI Ethics and Governance (4 Credits)

Course Description

This course introduces students to some of the central ethical issues in existing and emerging digital technologies, with an emphasis on the ethics of artificial intelligence (AI), as well as how these issues arise in the context of organizational governance and compliance. Students will explore topics in digital and AI ethics with respect to relevant professional areas-such as data science, computer science, software engineering, user experience and design, among others-as well as topics concerning the broader social implications of digital technologies and the ethical challenges they raise.

The goal of the course is to critically engage with these topics and cases interactively, studying both their theoretical, philosophical context and their practical implications, so that students can pursue continued, independent reflection on key issues in digital and AI ethics and apply the guiding ethical principles that emerge to their own professional and personal lives. In addition to addressing these ethical challenges, students will consider how organizations and institutions—corporations, IRBs, and legislative bodies—can or should respond to such challenges through regulation, oversight, or other mechanisms. Students will be encouraged to draw on their own professional experience in assessing key questions and cases in digital and AI ethics.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Demonstrate advanced knowledge of existing ethical issues in digital technologies and AI
  • Anticipate ethical issues arising from emerging digital technologies and developments in AI
  • Identify the philosophical bases for ethical concerns surrounding digital technologies and AI
  • Exhibit familiarity with and understanding of established ethical frameworks, concepts, and principles within ethical theory
  • Synthesize those theoretical frameworks, concepts, and principles and connect them to applied issues, using the theoretical resources to help understand and resolve the applied issues while at the same time scrutinizing the theoretical principles by evaluating their real-world implications
  • Evaluate competing considerations about engineers’ and designers’ moral responsibility for the products they create and services they provide
  • Engage in independent ethical reasoning on novel problems using theoretical and practical ethical resources learned
  • Foster ethical behavior and integrity in their professional and personal lives using the theoretical and practical resources learned
  • Develop concrete proposals for addressing ethical challenges in digital technologies and AI at the level of organizational governance

Course Topics

  • Ethical frameworks, concepts, and principles (consequentialism, deontology, rights, etc.)
  • Ethics of information, part I: privacy and transparency
  • Ethics of information, part II: intellectual property, individual liberties, and human rights
  • Algorithmic bias, “weapons of math destruction,” and social justice
  • The “black box” explainability problem in deep learning AI
  • Ethics of human-AI interaction and impact on social relationships (e.g., anthropomorphic framing in AI and robotics)
  • Digital technologies and human wellbeing: digital media and mental health
  • Digital technologies and democracy: digital media, filtering, misinformation, and political polarization
  • AI and human work: automation, worker displacement, and the meaning of work
  • Ethics of design and user experience: “dark patterns” and user agency
  • Ethics of data capture, digital advertising, and “surveillance capitalism”
  • Ethics of biometric identification
  • Data privacy and regulatory mechanisms: GDPR, HIPAA, IRB regulations, etc.
  • The internet, social media, and the question of legal status (e.g., public utility status, technology or publishing company status, etc.)
  • Artificial moral agency, part I: theory
  • Artificial moral agency, part II: application (e.g., ethics settings in driverless cars, constraints on autonomous weapons systems, etc.)

Coordinator: Dr. Andrew McAninch

Electives

CSC 5601—Theory of Machine Learning (4 Credits)

Course Description

This course provides a broad introduction to machine learning. Theory of machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from example inputs in order to make data-driven predictions or decisions, rather than following strictly static program instructions.

Topic categories include decision boundaries, optimization, and both supervised and unsupervised methods. Students will apply the theory to implementing and evaluating machine learning algorithms with hands-on, tutorial-oriented laboratory exercises.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Explain and analyze machine learning models and prediction algorithms (e.g., k-nearest neighbors, logistic regression, SVMs, decision trees) in a precise manner
  • Confidence in applying, manipulating, and interpreting linear algebra and calculus concepts within the context of machine learning
  • Implement and validate code for a mathematical model or algorithm given as an equation
  • Explain the geometric and algebraic interpretations of linear and non-linear decision boundaries and their relationship to error metrics (e.g., accuracy)
  • Understand the concepts of learning theory, i.e., what is learnable, bias, variance, overfitting, curse of dimensionality, splitting data for evaluation of model predictions
  • Estimate and plot decision boundaries described by trained models
  • Be able to encode non-numerical variables in tabular data as numerical features
  • Describe implications of feature representations with respect to linear separability
  • Apply approaches for engineering and evaluating new features from existing data
  • Derive, visualize, apply, and interpret loss functions and associated derivatives to assess the quality of model predictions and fit to data
  • Describe and implement model training in terms of naïve and gradient-driven search problems over parameter space
  • Compare and contrast technical requirements and computational efficiency of two unconstrained optimization algorithms (e.g., gradient descent, Newton’s method)

Prerequisites by Topic

  • Linear algebra
  • Python
  • NumPy
  • Functional programming

Coordinator: Dr. John Bukowy

CSC 5611—Deep Learning (4 Credits)

Course Description

This course provides an in-depth introduction to the foundations of deep learning. Students will learn how to architect, train, and evaluate deep neural networks. Students will gain experience with backpropagation, a variety of network structures, and a variety of options for training networks. This course is open to qualified undergraduates.

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

  • Understand the process of backpropagation and its role in training deep networks
  • Implement a basic deep learning network library
  • Apply deep learning to a unique dataset and analyze performance
  • Compare options for training deep neural networks, for example, optimization methods, generalization methods, normalization, initialization methods
  • Apply transfer learning to leverage pre-trained models
  • Compare various modern network architectures, for example, convolutional neural networks (CNNs), encoder-decoders, generative adversarial networks (GANs), or transformers.
  • Emphasis on topics can vary depending on the instructor’s specialties
  • Evaluate training methods and alternative architectures based on model accuracy, constraints, and training performance
  • Discuss the ethical implications of deep neural network applications
  • Compare the performance of the from-scratch deep neural network library implementation to an existing library when applied to a unique Dataset

Prerequisites by Topic

  • Machine learning
  • Python fundamentals

Coordinator: Dr. Josiah Yoder

CSC 5651—Deep Learning in Signal Processing (4 Credits)

Coordinator: Dr. Eric Durant

CSC 5241—GPU Programming (4 Credits)

Coordinator: Dr. Eric Durant

CSC 5980—Topics in Computer Science (Variable Credits)

Course Description

This course allows for study of emerging topics in computer science that are not present in the curriculum. Topics of mutual interest to faculty and students will be explored.

Coordinator: Dr. Derek Riley

CSC 6999—Computer Science Independent Study (Variable Credits)

Course Description

This course allows for study of emerging topics in computer science that are not present in the curriculum. Topics of mutual interest to faculty and students will be explored.

Coordinator: Dr. Derek Riley