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Hossein Khazaei
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Posts
Why Deep Learning
Published:
Deep learning has dominated the field of machine learning and artificial intelligence. But why? The reason is that it is simple so that many non-professionals can learn how to work with it in a short amount of time, and yet it is very effective, capable of solving problems that by no means was possible using classic methods.
Hyperparameter Tuning
Published:
It is important to use a separate validation dataset from the train and test sets for tuning model hyperparameters. (ref)
Ensemble Models
Published:
Ensemble is the art of combining diverse set of learners (Individual models) together to improvise on the stability and predictive power of the model. Roughly, ensemble learning methods, that often trust the top rankings of many machine learning competitions are based on the hypothesis that combining multiple models together can often produce a much more powerful model. Ensemble learning is a machine learning paradigm where multiple models (often called “weak learners”) are trained to solve the same problem and combined to get better results. Click for more info.
Any Deep Learning classifier is a form of Logistic Regression
Published:
Claim: Any deep learning classifier is a form of logistic regression. Click to see the reasoning behind this.
Machine Learning Universe: A Big Picture
Published:
There are many different algorithms in the machine learning universe. Each algorithm has its own intuition, use, advantages, and disadvantages. Click for more info.
project
User-User Collaborative Filtering
Published:
Summary: The goal is to desing a User-User Collaborative Filtering that we can use to predict how would a given user would rate a given movie that he/she has not seen before. The idea is to identify users with the most similar interactions profile (nearest neighbors) to that user and see how they rated that movie, and based on the similarity coefficients (for between users) that we calculate, we then predict the ratings. We can later on use such ratings to recommend new movies to the users. We use the 20 million MovieLens data set available on Kaggle. Though, for practical implementation on a pc we shrink this dataset.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Item-Item Collaborative Filtering
Published:
Summary: The goal is to desing a Item-Item Collaborative Filtering that we can use to predict how would a given user would rate a given movie that he/she has not seen before. The idea is to find items similar to the ones the user already “positively” interacted with. This method is said to be “item-centered” as it represents items based on interactions users had with them and evaluate distances between those items. We use the 20 million MovieLens data set available on Kaggle. Though, for practical implementation on a pc we shrink this dataset.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Matrix Factorization using Alternating Least Squares
Published:
Summary: The goal is to derive latent representation of the user and item feature vectors. The (predicted) ratings that a user gives to an item is the inner product of user’s latent vector and the item’s latent vector. We use alternating least squares for training. We use the 20 million MovieLens data set available on Kaggle. Though, for practical implementation on a pc we shrink this dataset.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Matrix Factorization using Embedding Layers
Published:
Summary: The goal is to derive latent representation of the user and item feature vectors. The (predicted) ratings that a user gives to an item is the inner product of user’s latent vector and the item’s latent vector. The idea here is to use the technique that we often used when we want to convert categorical variables into numerical vectors: Embedding. Keras has embedding layers that automatically learns the latent representation of such cases. We use the 20 million MovieLens data set available on Kaggle. Though, for practical implementation on a pc we shrink this dataset.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Matrix Factorization using Auto-Encoder
Published:
Summary: The goal is to derive latent representation of the user and item feature vectors. The (predicted) ratings that a user gives to an item is the inner product of user’s latent vector and the item’s latent vector. The idea here is to use autoencoder to get the latent representations. We use the 20 million MovieLens data set available on Kaggle. Though, for practical implementation on a pc we shrink this dataset.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Bayesian Bandit Recommender System.
Published:
Summary: We have several bandits that we do not know the success rate of any of them. We want to implement an algorithm that automatically balances the exploration-exploitation, and achieves finds the optimal bandit for us. The idea here is to use Bayesian Bandit algorithm to for choosing the bandits in a series of experiments.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Control of Cart Pole with a Policy Search
Published:
Task: The goal is to design a control policy to keep a Cart Pole leveled.
Solution: We assume a simple linear policy. We use a simple algorithm to find the optimal policy by brute-force policy search.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Control of Cart Pole with State-Action Value Functions
Published:
Task: The goal is to control a Cart Pole using value functions, particularly, Q-values.
Solution: We find state-action value functions (known also as Q-values) and use those for finding the optimal policy.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Control Policy for Mountain Car with Q-value Function Approximator
Published:
Task: The goal is to design a control policy for a car in a valley to get on the top of the valley as soon as possible.
Solution: We first use RBF kernels to map the features to higher feature space. We then assume a simple linear policy, and learn the state-action value functions (Q-values) to learn the optimal policy.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Finding Control Policy for Mountain Car using TD(n) for finding the Q-value Function Approximator
Published:
Task: The goal is to design a control policy for a car in a valley to get on the top of the valley as soon as possible.
Solution: Here we use the TD(n) for estimating the state-action values for different pairs of (state, action). Using such estimated values as training samples, we train a (linear) function approximator to estimate the state-action values (Q-values). Note that we use RBF kernels to map the features to higher feature space. This increases the performance of the model. After learning the state-action value functions (Q-values) we derive the optimal policy.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Finding Control Policy for Mountain Car using TD(λ) and elibility traces for finding the Q-value Function Approximator
Published:
Task: The goal is to design a control policy for a car in a valley to get on the top of the valley as soon as possible.
Solution: Here we use the TD(λ) for estimating the state-action values for different pairs of (state, action). The Eligibility Traces allow us to use a Backward-View implementation, which means that we do not need to wait until the end of episodes to calculate the updates. Using such estimated values as training samples, we train a (linear) function approximator (with some kernels to shift the feature space to a higher dimension space) to estimate the state-action values (Q-values).
For more information on this project, please see link. To see the Github repository for this project, see Github.
Policy Gradient with Baseline
Published:
Task: The goal is to directly model the policy function and try to optimize it. This approach is called policy gradient.
Solution: Here we model the policy function using a neural network, and try to optimize it. The policy gradient approach typically has hagh variance, and hence we use a technique called baseline to decrease the variance of the model. The baseline requires the calculating of the state value functions V(s). We use another neural network to calculate the value functions. The challenge of this project is to calculate the gradient when trying to optimize the policy function. Here we show a trick to do that.
For more information on this project, please see link. To see the Github repository for this project, see Github.
Policy Gradient with Baseline in Continuous Action Space
Published:
Task: The goal is to directly model the policy function and try to optimize it (i.e. policy gradient). The challenge is that we have continuous action space (i.e. infinite number of actions available to us), and hence the option of training one model per action is not available to us.
Solution: The trick we play is that we assume that the action comes from a Gaussian probability distribution function, and we estimate the parameters of that distribution function. We also use the baseline to help improving the performance of the model, and to do that, we use another neural network to estimate the state value functions V(s).
For more information on this project, please see link. To see the Github repository for this project, see Github.
Prediction model for COVID-19 Pandemic
Published:
In this project we develop a predicting model based on SEIR epidemiological model coupled with the replicator dynamics model. The Hospitalization data is used to make predictions on the pandemic.
For more information and some of the results, see link. To see the corresponding publication on the theoretical aspects of the model we used here, see link.
Machine Learning Algorithms for Solving Optimization Problems
Published:
In this project we use the domain knowledge + machine learning to solve large quadratic optimization problems with many inequalities. Knowing that the regions for the input parameters corresponding to each active set (class) are linearly separable, we leverage the rich body of classification algorithms to predict the active set at optimum, and use that to find the optimum. We use different classification algorithms, including LDA, neural networks, SVM, and XGBoost. Our simulations show high accuracies for LDA and neural networks for this classification task.
For more information, see link. To see the pdf file for the corresponding publication for the model, see link.
To see the Github repository for this project, see Github.
Simulating Pandemics with Multiple Waves
Published:
This project consists of the simulations we performed for the model we proposed for the pandemics. Watching COVID-19 pandemic we realized that the classic epidemiological models, such as SIS, SIR, SEIR, etc., fail to capture the dynamics of the pandemics, specifically, the potential for multiple waves of the disease. Here we modified the SEIR model to include the behavior of the individuals in the society as a part of the model.
For more information, see link. To see the pdf file for the corresponding publication for the model, see link.
To see the Github repository for this project, see Github.
Time-Series Forecast + Scenario Reduction + Stochastic Optimization for household with PV pandels and energy storage
Published:
For a house with photovoltaic (PV) panels and energy storage participating actively in buying/selling energy in two-settlement market, the problem it how to deal with the uncertainty of power generation of PV panels and the market prices. The solution is stochastic optimization. This approach characterizes the uncertainties as scenarios then tries to minimize the expected cost. In this project,
- LSTM is used to generate single forecasts about unknown market prices for the coming hours.
- CNN and is used to generate single forecasts about unknown demand for the coming hours.
- SARIMA is used to generate the benchmark for the forecasts of market prices and demand.
- The joint probability distribution function (pdf) of the forecast errors (during the training period) is used for generating forecast errors, and add them to the forecasts generated by CNN, LSTM, and SARIMA to generate the overall scenarios.
- A Simultaneous Backward Scenario Reduction is used to decrease the number of scenarios while keeping the most important information in the scenarios unchanged.
- with each new observation of the data, the conditional joint pdf of the forecast errors are calculated, and the new pdf is used to generate scenarios.
For more information on this project, please see link. To see the pdf file for a corresponding publication (where we published some of the results of this project), see link.
Iterative Approach to Solve Distributed Optimization for Coupled Intra-Market of Energy
Published:
Task: Imagine a intra-market between several regional markets, where the players of the intra-market are the operators of the regional markets. The goal of this intra-market is to facilitate trade between markets.
Challenge: How to clear this market such that the regional market operators reveal as little as possible information.
Solution: We formulate the problem as a distributed optimization problem, look at the minimum information needed to be exchanged in the market, especially the coupled regional markets, and through an iterative mechanism ensure that the outcome of this iterative approach makes the results of the intra-market converge to the optimal results.
For more information on this project, please see link. To see the Github repository for this project, see Github.
publications
Forecating of COVID-19 Pademic Using Coupled SEIR and Replicator-Dynamics Model
Published in , 2015
Authors: Hossein Khazaei, Alfredo Garcia, Ceyhun Eksin
Task: To predict the trajectory, number of infectious, and most importantly, the number of hospitalized individuals for COVID-19 pandemic.
Summary: We proposed a coupled SEIR-replicator dymanics model that is capable of capturing the dynamics of the disease. Here we modified the model to be suitable to be applied to the real-world data, test it, and observed that the proposed model can accurately capture the dynamics of the pandemic, and make forecasts for the hospitalizations.
For more information and see some of the simulations, see link.
Physics-Aware Fast Learning and Inference for Predicting Active Set of DC-OPF
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Task: To use machine learning methods to solve large optimization problems.
Summary: Motivated by the fact that identifying a set of active constraints in an optimization problem can significantly improve our capabilities in solving it, in this paper we investigate the idea of predicting binding constraints, referred to as active sets, in quadratic optimization problems, and then solving the new reduced optimization problem.
The Optimization problem we look into in the DC-OPF, widely used in electricity markets and power system operations. We show that the regions for the classes in this problem are linearly separable, and hence algorithms like SVM and LDA should work very well. LDA in particular achives very good results considering the fact that its training and evaluation time are really fast. For more information and see some of the simulations, see link. To see the pdf of the paper, see link.
A Market Mechanism for Trading Flexibility Between Interconnected Electricity Markets
Published in , 2015
Authors: Hossein Khazaei, Ceyhun Eksin, Alfredo Garcia
Task: To design and implement an intra-market over regional markets where regional market operators are able share very limited amount of information while ensuring the efficiency.
Summary: We designed a market mechanism, which in essense is a distributed optimization problem, that in an iterative approach the market can converge to the optimal results. For more information and see some of the simulations, see link.
Disease spread coupled with evolutionary social distancing dynamics can lead to growing oscillations
Published in , 2015
Authors: Hossein Khazaei, Keith Paarporn, Alfredo Garcia, Ceyhun Eksin
Task: To design a model for the pandemic that can captures multiple waves of the disease.
Summary: Classic epidemiological models such as SIR, SIS, and SEIR fail to capture the multiple waves of the pandemic. Observing that it is the behavior of the individuals in the society and the governmental policies that causes multiple waves of the disease, we propose a model that capture such factors into consideration.
The proposed model consists of a standard SEIR model and a replicator dynamics model that are connected with two feedback loops. The SEIR model captures the dynamics of the disease while the replicator dynamics model captures the behavior of the individuals in the society in a game-theoric framework.
The results show that the proposed model is well capable of capturing different waves of the pandemic.
For more information, see link. To see the pdf of the paper, see link.
Stochastic Decision-Making Model for Aggregation of Residential Units with PV-Systems and Storages
Published in , 2015
Authors: Hossein Khazaei, Ramin Moslemi, Ratnesh Sharma
Task: To design optimal energy procuring model for households with PV panelds and energy storage.
Summary: We propose a scenario based stochastic optimization framework for optimal decision making for households. The proposed model
- Uses Seasonal Autoregressive Integrated Moving Average (SARIMA) to generate forecasts for the energy prices and the power produced by the PV panels.
- The joint probability distribution function (pdf) of the forecast errors are used to generate (forecast error) scenarios and add them to the forecasts to create the scenarios (for the market prices and the PV generations).
- We use gaussian probability distribution functions to model the forecast errors. This significantly decreases the computational burden as the conditional probability distribution function for a Gaussian pdf has a closed form formula.
- We further use Simultaneous Backward Scenario Reduction to decrease the number of scenarios while keeping the information of the important scenarios as much as possible.
- With the arrival of any new observation of the unknown variables (i.e. power generation of PV panels, and market prices, for some hours), the conditional pdf of the random variables are updates, new scenarios are generated, and new decisions are made. For more information, see link. To see the pdf of the paper, see link.
On the Market Equilibria with Renewable Power Producers in Power Networks
Published in , 2015
Authors: Hossein Khazaei, Andy Sun, Yue Zhao
Task: To design a two-settlement market (forward/spot markets) that the operator can implement it in reality, and achieves optimality.
Summary: We propose a two settlement market for stochastic renewable power producers (RPPs) that
- The bid format of the stochatic RPPs is compatible to non-stochastic energy resources, and the system operator can use its conventional tools to operate the system optimally.
* There exists a computationally feasible method for finding the Nash equilibrium in the game. We detail this algorithm in the paper.
For more information, see link. To see the pdf of the paper, see link.
Indirect Mechanism Design for Efficient and Stable Renewable Energy Aggregation
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Task: Design an aggregation mechanism that achieves a set of desired ex-ante (in expectation) and ex-post desired properties.
Summary: Motivated by the competitive equilibrium (CE) of a specially formulated market with transferrable payoff, we design a aggregation model that:
- Asking for very limited information (a single number) from the stochastic renewable power producers, and yet able to achieve a wide range of desired properties.
* Exitence of a unique Nash equilibrium with closed form formula (ex-ante and ex-post) - In-core payments from the point of view of cooperative game theory (ex-ante and ex-post)
- No collusion (ex-ante and ex-post).
- Optimality (compared to the ideal case where the aggregator knows all the private information of the members).
For more information, see link. To see the pdf of the paper, see link.
Two-Level Decision Making Model for A Distribution Company in Day-Ahead Market
Published in , 2015
Authors: Hossein Khazaei, Behrooz Vahidi, Seyed Hossein Hosseinian, Hasan Rastegar
Task: To design a decision making model for a utility (distribution company) to buy energy from forward market and sell it to customers.
Summary: We propose a two-level model for which in the upper level the buying step is modeled and in the lower level, the selling step is modeled. We modeled the problem as a game for which we significantly decreased the size of the problem. Finally, we used reinforcement learning to find the equilibrium in this game.
For more information, see link. To see the pdf of the paper, see link.
An Incentive Compatible Market Mechanism for Integrating Demand Response into Power Systems
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Task: To design a market mechanism for demand response to participate in two-settlement forward/spot markets.
Summary: Each demand response providers bids her demand reduction capacity and cost rate, and the system operator schedules the power dispatch to minimize the overall system cost. We show that, with the proposed mechanism, truthful bidding by the demand response providers is achieved at a Nash equilibrium (NE), and as a result, the social welfare is maximized.
For more information, see link. To see the pdf of the paper, see link.
A Simple Market Mechanism For Renewable Power Producers Achieves Asymptotic Social Efficiency
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Summary: Here we prove that the Nash equilibria of the simple forward market mechanism we proposed before (see here) asymptotically converges to the social optimality.
For more information, see link. To see the pdf of the paper, see link.
Competitive Market with Renewable Power Producers Achieves Asymptotic Social Efficiency
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Task: To design forward market for intermittent renewable energy resources to bid into it. What is the challenge? Intermittency. If the renewable energy resources do not know how much they can deliver, how can they in a forward market?
Goal: The goal is to design a market that at there exists an ex-post Nash equilibrium where the social optimality is maximized.
For more information, see link. To see the pdf of the paper, see link. The codes can be found in a Github repository in link.
A Simple Payoff Allocation Mechanism Achieves Efficiency And Stability In Renewable Energy Aggregation
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Goal: To design aggregation mechanisms for renewable power producers that guarantees no collusion among the members of the aggregation.
For more information, see link. To see the pdf of the paper, see link.
Ex-post Stable and Fair Payoff Allocation for Renewable Energy Aggregation
Published in , 2015
Authors: Hossein Khazaei, Yue Zhao
Task: Aggregating statistically diverse renewable power producers (RPPs) is an effective way to reduce their overall uncertainty. The question is: How to do this?
Goal: In this paper the goal is four-fold: (1) To extract as little information as possible (for example do not extract the probability distribution function. It’s a lot of data and how to aggregate a bunch of such data is itself quite problematic) (2) each group of renewable power producers has incentive to stay in the coalition (group rationality), (3) to ensure the truthfulness of the submitted information of the members, and (4) that the payment mechanism achieves budget balance, meaning that the aggregator doesn’t keep anything for itself.
For more information, see link. To see the pdf of the paper, see link.
An Incentive Compatible Profit Allocation Mechanism for Renewable Energy Aggregation
Published in , 2015
Authors: Yue Zhao, Hossein Khazaei
Task: To define a comprehensive mechanism for aggregating renewable power producers, coordinate them, solicit information from them, represent the aggregation in the market on behalf of the renewable power producers, and distribute the payoffs among the members.
Goal: In this paper the goal is four-fold: (1) The performance of the aggregator, as a whole, is optimized, (2) each single renewable power producer has incentive to stay (individual rationality), (3) to ensure the truthfulness of the submitted information of the members, and (4) that the payment mechanism achieves budget balance, meaning that the aggregator doesn’t keep anything for itself.
For more information, see link. To see the pdf of the paper, see link.
A New Transmission Expansion Planning Framework and Cost Allocation Method Considering Financial Transmission Rights
Published in , 2015
Authors: Hossein Khazaei, Moein Sabounchi
Task: Transmission system in power grids is a public service. The question is: How to allocate the costs of planning and expanding the transmission systems among the generators, utilities, and finally the customers.
Goal: The transmission system is a public service available to all members of the grid. However some benefit more from it comparing to others. In allocating the costs, we need to be fair.
For more information, see link. To see the pdf of the paper, see link.
A New Method for Equilibrium Selection in Financial Transmission Right’s Auctions
Published in , 2015
Authors: Hossein Khazaei, Moein Sabounchi
Task: To define a criteria for selecting equilibrium in auctions, specifically, the Financial Transmission Right’s auction.
Goal: To select an equilibrium that is (1) on the Pareto curve, (2) to quantify the tradeoff between different equilibria, and (3) to include the likelihood of the equilibrium into account
For more information, see link. To see the pdf of the paper, see link.
A New Residential Demand Response Management Method Based on a Social Welfare Optimization Framework
Published in , 2015
Authors: Moein Sabounchi, Hossein Khazaei, Seyed Kamal Hosseini Sani
Task: To design policies such that (electricity) consumers participate in demand response projects.
Goal: To achieve welfare maximization.
For more information, see link. To see the pdf of the paper, see link.
talks
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.