diff --git a/README.md b/README.md index 45c202063a374..e4741ae9704d6 100644 --- a/README.md +++ b/README.md @@ -2,7 +2,7 @@ # Jekyll Now -**Jekyll** is a static site generator that's perfect for GitHub hosted blogs ([Jekyll Repository](https://github.com/jekyll/jekyll)) +**Jekyll** is a for fix static site generator that's perfect for GitHub hosted blogs ([Jekyll Repository](https://github.com/jekyll/jekyll)) **Jekyll Now** makes it easier to create your Jekyll blog, by eliminating a lot of the up front setup. diff --git a/_config.yml b/_config.yml index d4916414195c9..ba8a32bc022d7 100644 --- a/_config.yml +++ b/_config.yml @@ -1,86 +1,67 @@ +# Welcome to Jekyll! # -# This file contains configuration flags to customize your site +# This config file is meant for settings that affect your whole blog, values +# which you are expected to set up once and rarely edit after that. If you find +# yourself editing this file very often, consider using Jekyll's data files +# feature for the data you need to update frequently. # +# For technical reasons, this file is *NOT* reloaded automatically when you use +# 'bundle exec jekyll serve'. If you change this file, please restart the server process. -# Name of your site (displayed in the header) -name: Your Name +# Site settings +title: Rsekaii +author: Rames Nagib AlJneibi +email: r.n.j@hotmail.com +description: >- + Exploring my love for mathematics, and my personal growth -# Short bio or description (displayed in the header) -description: Web Developer from Somewhere +# Posts +show_excerpts: true -# URL of your avatar or profile pic (you could use your GitHub profile pic) -avatar: https://raw.githubusercontent.com/barryclark/jekyll-now/master/images/jekyll-logo.png +# URL +baseurl: "" # the subpath of your site, e.g. /blog +url: "https://rsekaii.github.io" # the base hostname & protocol for your site, e.g. http://example.com -# -# Flags below are optional -# - -# Includes an icon in the footer for each username you enter -footer-links: - dribbble: - email: - facebook: - flickr: - github: barryclark/jekyll-now - instagram: - linkedin: - pinterest: - rss: # just type anything here for a working RSS icon - twitter: jekyllrb - stackoverflow: # your stackoverflow profile, e.g. "users/50476/bart-kiers" - youtube: # channel/ or user/ - googleplus: # anything in your profile username that comes after plus.google.com/ +# Social +github_username: rsekaii -# Enter your Disqus shortname (not your username) to enable commenting on posts -# You can find your shortname on the Settings page of your Disqus account +# Disqus Comments disqus: + # Leave shortname blank to disable comments site-wide. + # Disable comments for any post by adding comments: false to that post's YAML Front Matter. + shortname: rames -# Enter your Google Analytics web tracking code (e.g. UA-2110908-2) to activate tracking -google_analytics: - -# Your website URL (e.g. http://barryclark.github.io or http://www.barryclark.co) -# Used for Sitemap.xml and your RSS feed -url: - -# If you're hosting your site at a Project repository on GitHub pages -# (http://yourusername.github.io/repository-name) -# and NOT your User repository (http://yourusername.github.io) -# then add in the baseurl here, like this: "/repository-name" -baseurl: "" - -# -# !! You don't need to change any of the configuration flags below !! -# - -permalink: /:title/ +# Google Analytics +google_analytics: G-7S88B0TLVJ -# The release of Jekyll Now that you're using -version: v1.2.0 - -# Jekyll 3 now only supports Kramdown for Markdown +# Build settings +markdown: kramdown kramdown: - # Use GitHub flavored markdown, including triple backtick fenced code blocks - input: GFM - # Jekyll 3 and GitHub Pages now only support rouge for syntax highlighting - syntax_highlighter: rouge - syntax_highlighter_opts: - # Use existing pygments syntax highlighting css - css_class: 'highlight' + math_engine: mathjax + +# theme: minima +remote_theme: jekyll/minima +minima: + skin: auto + +plugins: + - jekyll-feed + - jekyll-remote-theme + + +# Exclude from processing. +# The following items will not be processed, by default. Create a custom list +# to override the default setting. +# exclude: +# - Gemfile +# - Gemfile.lock +# - node_modules +# - vendor/bundle/ +# - vendor/cache/ +# - vendor/gems/ +# - vendor/ruby/ -# Set the Sass partials directory, as we're using @imports sass: - style: :expanded # You might prefer to minify using :compressed - -# Use the following plug-ins -gems: - - jekyll-sitemap # Create a sitemap using the official Jekyll sitemap gem - - jekyll-feed # Create an Atom feed using the official Jekyll feed gem - -# Exclude these files from your production _site -exclude: - - Gemfile - - Gemfile.lock - - LICENSE - - README.md - - CNAME + sass_dir: _sass + style: compressed diff --git a/_includes/contact.html b/_includes/contact.html new file mode 100644 index 0000000000000..663d068807a07 --- /dev/null +++ b/_includes/contact.html @@ -0,0 +1,52 @@ + +
+ Profile Photo +
+ +

Contact

+
+ + + + 📧 r.n.j@hotmail.com + + + + + 🐙 github.com/Rsekaii + + + + + 💼 LinkedIn Profile + + + + + 📸 @rsekaii + +
+ + +
+ + 📄 My CV + +
+ + +
+

📜

+
+ “All Nature is but Art, unknown to thee;

+ + All chance, direction, which thou canst not see;

+ + All discord, harmony not understood;

+ + All partial evil, universal good.” +
+

+ — Alexander Pope, An Essay on Man (1733) +

+
diff --git a/_includes/footer.html b/_includes/footer.html new file mode 100644 index 0000000000000..db72885e91f20 --- /dev/null +++ b/_includes/footer.html @@ -0,0 +1,35 @@ +
+ + +
+ +

{{ site.title | escape }}

+ +
+
+
    +
  • + {%- if site.author -%} + {{ site.author | escape }} + {%- else -%} + {{ site.title | escape }} + {%- endif -%} +
    • + {%- if site.email -%} +
  • {{ site.email }}
    • + {%- endif -%} +
+
+ +
+ {%- include social.html -%} +
+ +
+

{{- site.description | escape -}}

+
+
+ +
+ +
diff --git a/_includes/head.html b/_includes/head.html new file mode 100644 index 0000000000000..aca6b4ff59805 --- /dev/null +++ b/_includes/head.html @@ -0,0 +1,25 @@ + + + + + {%- seo -%} + + {%- feed_meta -%} + + {%- if jekyll.environment == 'production' and site.google_analytics -%} + {%- include google-analytics.html -%} + {%- endif -%} + + + + + diff --git a/_includes/header.html b/_includes/header.html new file mode 100644 index 0000000000000..d64a9f31dd85f --- /dev/null +++ b/_includes/header.html @@ -0,0 +1,29 @@ + diff --git a/_includes/mathjax.html b/_includes/mathjax.html new file mode 100644 index 0000000000000..df5304097f7af --- /dev/null +++ b/_includes/mathjax.html @@ -0,0 +1,12 @@ + + diff --git a/_layouts/default.html b/_layouts/default.html index b2939c0bc4483..a114b90d5556c 100644 --- a/_layouts/default.html +++ b/_layouts/default.html @@ -1,51 +1,73 @@ - - - {% if page.title %}{{ page.title }} – {% endif %}{{ site.name }} – {{ site.description }} - - {% include meta.html %} - - - - - - - - - - -
-
-
- - -
-

{{ site.name }}

-

{{ site.description }}

-
- - -
-
-
+ + + {%- include head.html -%} -
- {{ content }} + + {%- include header.html -%} + + +
+ 🏠
-
-
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- {% include svg-icons.html %} -
+
+
+ + + + + +
+ {{ content }} +
+ + + +
-
+ - {% include analytics.html %} + {%- include footer.html -%} + diff --git a/_posts/2014-3-3-Hello-World.md b/_posts/2014-3-3-Hello-World.md deleted file mode 100644 index d4665b6d18e9e..0000000000000 --- a/_posts/2014-3-3-Hello-World.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -layout: post -title: You're up and running! ---- - -Next you can update your site name, avatar and other options using the _config.yml file in the root of your repository (shown below). - -![_config.yml]({{ site.baseurl }}/images/config.png) - -The easiest way to make your first post is to edit this one. Go into /_posts/ and update the Hello World markdown file. For more instructions head over to the [Jekyll Now repository](https://github.com/barryclark/jekyll-now) on GitHub. \ No newline at end of file diff --git a/_posts/2025-04-08-aboutme b/_posts/2025-04-08-aboutme new file mode 100644 index 0000000000000..f6ff5f24d66e1 --- /dev/null +++ b/_posts/2025-04-08-aboutme @@ -0,0 +1,51 @@ +--- +layout: default +--- + +# Rames Nagib AlJneibi - رامس نجيب الجنيبي + +Welcome to my personal academic blog and portfolio. I’m currently pursuing a Master’s in Machine Learning and preparing for a PhD in Applied Mathematics. I’m passionate about uncovering deep structures in data and mathematics and applying them to real-world systems. + +I previously earned my Master’s in Mathematics and a Bachelor’s in Chemical Engineering. Professionally, I’ve worked across engineering, planning, and strategic roles in the Gas Business where I integrate technical expertise with long-term energy outlooks. + +## Research & Interests + +My academic and professional interests lie at the intersection of: + +- **Machine Learning & Time-Series Forecasting** +- **Optimization & Applied Mathematics** +- **Uncertainty Quantification and Conformal Prediction** +- **Energy Systems Planning & Gas Infrastructure** +- **Stochastic PDEs and Mathematical Modeling** + + +I’m currently focusing my Master’s thesis on **Conformal Prediction and Uncertainty Quantification**, while also exploring the intersection of **Numerical Methods for PDEs** and **Machine Learning**. + +My broader ambition is to contribute to the development of rigorous, real-world **mathematical models of physical systems**, bridging theory and application in meaningful ways. + +## Vision + +I believe that robust mathematical thinking is a superpower in today’s world — and I’m working toward becoming a **pioneer in data-driven decision-making** for energy and industrial systems. My goal is to lead impactful, intelligent solutions in one of the most critical sectors for global development. + +## Professional History + +- Senior Specialist – Gas Master Planning (Energy Sector) (2024-current) +- Senior Production Planning Engineer – ADNOC Gas (2022-2024) +- Process Engineer – ADNOC Refining (2019-2021) + +## Academic Journey + +While working full-time in a demanding technical and strategic role, I pursued my Master’s in Mathematics — and later began a second Master’s in Machine Learning. Despite the load of being a Full-Time student and Full-time Employee, I maintained strong academic performance while receiving promotions and high evaluations at work. That period tested and shaped my discipline, mental resilience, and passion for growth. + +It was during this time that I realized my ability to thrive at the intersection of theory and application — and it continues to fuel my vision for impactful, cross-disciplinary work. + + +## Personal Notes + +I’ve always loved helping others learn — whether as an older sibling, classroom tutor, or mentor — and I enjoy breaking down complex ideas into simple, digestible insights. + +My love for adventure and challenge extends beyond the academic realm. I’m into fitness and pursue my physical goals with the same discipline I apply to my intellectual ones. I primarily focus on bodybuilding, but I also enjoy long-distance running (even if I barely survive marathons) and challenging hikes that push my limits. + +There’s something deeply fulfilling about navigating both mind and body through effort and discomfort — and coming out stronger on the other side. + + diff --git a/_posts/academic/.gitkeep b/_posts/academic/.gitkeep new file mode 100644 index 0000000000000..8b137891791fe --- /dev/null +++ b/_posts/academic/.gitkeep @@ -0,0 +1 @@ + diff --git a/_posts/academic/2025-04-05-uncertainity-stat.md b/_posts/academic/2025-04-05-uncertainity-stat.md new file mode 100644 index 0000000000000..3a9e177878fa2 --- /dev/null +++ b/_posts/academic/2025-04-05-uncertainity-stat.md @@ -0,0 +1,103 @@ +--- +layout: post +title: " Uncertainty and Some Foundations of Statistical Inference" +date: 2025-04-05 +math: true +--- + +## Introduction + +This is an attempt to start writing about my research and learning journey throughout my master's in search of my master's thesis topic. + +As instructed and supported by **Doctor**, starting this post will help me develop the habit of writing and formulating everything I learn and come across that may benefit my thesis. + +**Doctor** gave me a number of introductory papers to initiate the process, and with that, I have started. + +--- + +## Uncertainty in Machine Learning + +### Aleatoric vs. Epistemic Uncertainty + +Aleatoric uncertainty is **irreducible**: it is intrinsic to the quantity we are measuring. No matter how much additional data we collect, it remains. + +Epistemic uncertainty is **reducible**: it arises from data/model limitations and can be reduced with more data or better modeling. + +--- + +### Formal Definitions + +Let \( x \in X \) be inputs and \( y \in Y \) outputs. + +#### Aleatoric Uncertainty: + +\[ +Y \mid x \sim f_{Y|x}(y \mid x) +\] + +#### Epistemic Uncertainty: + +Defined as the remaining uncertainty not captured by aleatoric uncertainty. It can be decomposed further into model, data, and estimation uncertainties. + +#### Total Uncertainty: + +\[ +\text{Total Uncertainty} = \text{Aleatoric Uncertainty} + \text{Epistemic Uncertainty} +\] + +## Statistical Knowledge +*Statistical & Probabilistic Inference in ML* + +### Kullback–Leibler Divergence + +Measures the "distance" between two distributions \( P \) (true) and \( Q \) (approximation): + +\[ +\text{KL}(P \parallel Q) = \sum P(x) \log \frac{P(x)}{Q(x)} \quad \text{(discrete)} +\] +\[ +\text{KL}(P \parallel Q) = \int P(x) \log \frac{P(x)}{Q(x)} dx \quad \text{(continuous)} +\] + +> KL divergence is **not symmetric**, and equals zero only when \( P = Q \). + +--- + +### Fisher Information + +Quantifies how much information a sample provides about a parameter. + +#### Definitions: + +1. **Variance of the Score Function**: + +\[ +I(\theta) = \mathbb{E} \left[ S(\theta) S(\theta)^T \right] +\quad \text{where } S(\theta) = \frac{\partial}{\partial \theta} \log p(X | \theta) +\] + +2. **Negative Expectation of the Hessian**: + +\[ +I(\theta) = -\mathbb{E} \left[ \frac{\partial^2}{\partial \theta \partial \theta^T} \log p(X | \theta) \right] +\] + +--- + +#### Interpretation: + +- **High Fisher Info** → Low uncertainty in \( \hat{\theta} \) +- **Low Fisher Info** → High uncertainty + +--- + +### Cramér-Rao Lower Bound: + +\[ +\text{Var}(\hat{\theta}) \geq I(\theta)^{-1} +\] + +The inverse of Fisher Information provides a lower bound on the variance of any unbiased estimator. + +--- + diff --git a/_posts/academic/2025-04-07-gaussian-processes.md b/_posts/academic/2025-04-07-gaussian-processes.md new file mode 100644 index 0000000000000..1231758fa9c07 --- /dev/null +++ b/_posts/academic/2025-04-07-gaussian-processes.md @@ -0,0 +1,244 @@ +--- +layout: post +title: "Gaussian Processes - From Concept to Implementation" +date: 2025-04-07 +math: true +--- + + + +## Introduction + +I noticed that writing about my academic journey helps solidify my understanding and provides my future self with a well-established reference whenever I need to recall something. + +Thus, whenever I learn something interesting, I will document it here. Whether it will be directly related to my Master's research will be decided later. + +Moreover, I will also include concepts that are related but that I do not fully understand. This paper will help me understand them thoroughly—or so I hope. + +--- + +## Gaussian Processes + +We typically assume a model of the form: + +$$ +y = w_0 + w_1 x + \text{noise} +$$ + +where \( w_0, w_1 \) are parameters to learn. + +A **Gaussian Process (GP)** makes no such assumption—it is non-parametric and assumes a distribution over functions. That is: + +- We assume the true function lies in an infinite space of functions. +- We constrain this space using training data. +- Then we assume a **multivariate Gaussian distribution** over any finite collection of function values. + +> *Note: It's not the function itself that's Gaussian, but any finite collection of its values is.* + +--- + +### How Do We Constrain the Space of Functions? + +Using **covariance** between function values at different training points, typically defined through a **kernel function** like the **RBF kernel**. + +--- + +### The Power of Normality + +Given a test point \( x_* \), we can infer the most probable function value \( f(x_*) \) using the normality assumption. + +--- + +### Why Is the Function Gaussian? + +Enter **Bayesian Modeling**. + +#### Likelihood: + +$$ +p(D_n \mid w) = \prod_{i=1}^{n} p(y_i \mid x_i, w) +$$ + +#### Prior: + +$$ +w \sim p(w) +$$ + +#### Posterior: + +$$ +p(w \mid D_n) +$$ + +#### Predictive Distribution: + +$$ +p(y \mid x, D_n) = \int p(y \mid x, w) p(w \mid D_n) \, dw +$$ + +--- + +### The GP Prior + +$$ +f(x) \sim \mathcal{N}(m(x), K(x, x')) +$$ + +- \( m(x) \): mean function +- \( K(x, x') \): kernel (covariance function) + +--- + +### Likelihood: + +$$ +y = f(x) + \epsilon, \quad \epsilon \sim \mathcal{N}(0, \sigma^2) +$$ + +--- + +### GP Prediction: + +Assuming: + +$$ +\begin{bmatrix} f(X) \\ f(x_*) \end{bmatrix} \sim \mathcal{N} +\left( 0, +\begin{bmatrix} K(X, X) & K(X, x_*) \\ +K(x_*, X) & K(x_*, x_*) \end{bmatrix} \right) +$$ + +Then: + +$$ +f(x_*) | X, y, x_* \sim \mathcal{N}(\mu_*, \sigma_*^2) +$$ + +where: + +$$ +\mu_* = K(x_*, X) [K(X, X) + \sigma_n^2 I]^{-1} y +$$ + +$$ +\sigma_*^2 = K(x_*, x_*) - K(x_*, X) [K(X, X) + \sigma_n^2 I]^{-1} K(X, x_*) +$$ + +--- + +## Why Gaussianity? + +### Central Limit Theorem (CLT) + +The GP prior is a generalization of CLT: the sum of many independent RVs tends toward Gaussianity. + +### Gaussian Likelihood: + +$$ +p(y_i \mid f(x_i)) = \mathcal{N}(f(x_i), \sigma^2) +$$ + +--- + +### Properties of Gaussian Distributions + +- Any subset of a joint Gaussian is Gaussian. +- Conditional distributions of Gaussians are Gaussian. +- Prior × Likelihood = Posterior is still Gaussian. + +--- + +## Application in Python + +We use the [`GPy`](https://sheffieldml.github.io/GPy/) library. + +### Data: + +```python +N = 10 +X = np.linspace(0.05, 0.95, N).reshape(-1, 1) +Y = -np.cos(np.pi * X) + np.sin(4 * np.pi * X) + \ + np.random.normal(loc=0.0, scale=0.1, size=(N, 1)) +``` + +### Kernel Setup + +RBF Kernel: + +$$ +k(x, y) = \sigma^2 \exp\left ( -\dfrac{\|x - y\|^2}{2l^2} \right ) +$$ + +```python +input_dim = 1 +variance = 1 +lengthscale = 0.2 +kernel = GPy.kern.RBF(input_dim, variance=variance, lengthscale=lengthscale) +model = GPy.models.GPRegression(X, Y, kernel) +``` + +--- + +## Kernel Parameter Optimization + +### Mathematical Form: + +$$ +k(x, x') = \sigma^2 \exp \left( - \frac{\|x - x'\|^2}{2 l^2} \right) +$$ + +- \( \sigma^2 \): overall scale (variance) +- \( l \): how quickly the function varies + +![lengthscale impact]({{ "/images/lengthscale-covariance.png" | relative_url }}) + +--- + +### GPy Optimization + +```python +model = GPy.models.GPRegression(X, Y, kernel) +model.optimize() +``` + +--- + +### Noise as Regularization + +```python +N = 40 +X = np.linspace(0.05, 0.95, N).reshape(-1, 1) +Y = -np.cos(np.pi * X) + np.sin(4 * np.pi * X) + \ + np.random.normal(loc=0.0, scale=0.5, size=(N, 1)) + +model = GPy.models.GPRegression(X, Y, kernel) +model.optimize() + +model.Gaussian_noise.variance.fix(0.01) +model.optimize() +``` + +**Comparison of high vs low noise:** + +
+ High noise + Low noise +
+ +--- + +## RBF Limitations + +### Complex function: + +![Complex function]({{ "/images/complexK.png" | relative_url }}) + +### Oversmoothing: + +![Oversmooth]({{ "/images/RBF2.png" | relative_url }}) + +### Oscillation: + +![Oscillating]({{ "/images/RBF1.png" | relative_url }}) + diff --git a/_posts/academic/2025-04-08-conformal-prediction.md b/_posts/academic/2025-04-08-conformal-prediction.md new file mode 100644 index 0000000000000..888903da9a007 --- /dev/null +++ b/_posts/academic/2025-04-08-conformal-prediction.md @@ -0,0 +1,131 @@ +--- +layout: post +title: "Conformal Prediction - Uncertainty Quantification in Practice" +date: 2025-04-08 +math: true +--- + +## Conformal Prediction + +Conformal prediction is a methodology for quantifying uncertainty and producing prediction intervals — similar in spirit to confidence intervals. + +Before diving into it, it’s important to understand a key idea: + +--- + +### Scoring Rule + +A **scoring rule** evaluates how well a predicted probability distribution aligns with an observed value. + +This concept is related to, but distinct from: + +- **Loss Functions**: Penalize prediction errors during training. +- **Scoring Functions**: Summarize model performance (like accuracy). +- **Scoring Rules**: Evaluate probabilistic forecasts directly. + +--- + +## Understanding Conformal Prediction + +The paper "A Tutorial on Conformal Prediction" by the authors Vovk, Gammerman, and Shafer (who were the orignators of the concept) +is a thorough paper for anyone interested, they also gracefull made a supplementary video breaking it down. +However, here I try to explain it in my own words. So don't expect the same level of detail. + +--- + +### Conformal Prediction Pipeline + +The pipeline helped make the method intuitive: + +1. **Define Uncertainty** + We begin by deciding what "uncertainty" we want to quantify from our model. + +2. **Score Function** + A nonconformity score function is used to quantify how far a predicted value is from the true value. A well-designed score function gives: + + \[ + s(\hat{y}, y) + \] + + Higher scores → more uncertainty. Lower scores → greater conformity. + + > ⚠️ Note: This “score function” differs from the Fisher score or scoring rule — terminology can be confusing. + +3. **Calibration Scores and Quantile Threshold** + Using a **calibration set**, we compute scores and determine the quantile threshold: + + \[ + \hat{q} = \frac{(n+1)(1-\alpha)}{n} + \] + + For instance, \( \alpha = 0.05 \) gives a 95% confidence level. + Now \( \hat{q} \) is the threshold such that ~95% of calibration scores fall below it. + +4. **Prediction Set** + Given a test point, we define the prediction set as: + + \[ + C(X_{\text{test}}) = \{ y \mid s(\hat{y}_{\text{test}}, y) \leq \hat{q} \} + \] + + This means: with 95% confidence, the true \( y \) is in this prediction set. + +--- + +## Key Takeaways + +Conformal prediction is **model-agnostic** and **distribution-free**. + +However, success depends on: + +- A well-chosen **score function** +- The assumption that data is **exchangeable** +-- +### What is Exchangeability? + +In probability, a sequence of random variables is **exchangeable** if the joint distribution does not change when the order of the variables is shuffled. + +Formally: +\[ +P(X_1, X_2, \dots, X_n) = P(X_{\pi(1)}, X_{\pi(2)}, \dots, X_{\pi(n)}) +\] +for any permutation \( \pi \) of indices. + +This is **weaker than the i.i.d. assumption** — all i.i.d. sequences are exchangeable, but not all exchangeable sequences are i.i.d. + +**Why it matters:** +Conformal prediction only requires exchangeability, not full independence, making it more broadly applicable in real-world data where some dependencies exist. + + + +--- + +## Application: Tumor Segmentation + +One practical application shared by the authors involves detecting gut polyps from endoscopy images. + +### Procedure Summary + +- A subset of the data is used for calibration. +- A **target TPR (True Positive Rate)** of \( 1 - \alpha \) is set. +- FNR is defined as: + +\[ +\text{FNR} = 1 - \frac{\sum (\text{Predicted Mask} \cap \text{Ground Truth Mask})}{\sum (\text{Ground Truth Mask})} +\] + +- Softmax scores are used as uncertainty scores. +- A threshold \( \lambda_{\text{hat}} \) is computed using **Brent’s method**: + +\[ +\text{FNR}(\lambda) - \left(\frac{n+1}{n} \alpha - \frac{1}{n}\right) = 0 +\] + +- Applying \( \lambda_{\text{hat}} \) yields segmentation masks that satisfy the desired confidence level. + +--- + +## Final Thoughts + +Despite its simplicity, conformal prediction delivers surprisingly powerful results. Its guarantee of coverage, even without assumptions about the model or distribution, makes it one of the most elegant tools in the uncertainty quantification toolbox. + diff --git a/_posts/personal/.gitkeep b/_posts/personal/.gitkeep new file mode 100644 index 0000000000000..8b137891791fe --- /dev/null +++ b/_posts/personal/.gitkeep @@ -0,0 +1 @@ + diff --git a/_posts/personal/2024-04-08-prediction-of-feed-yields.md b/_posts/personal/2024-04-08-prediction-of-feed-yields.md new file mode 100644 index 0000000000000..135897d309c85 --- /dev/null +++ b/_posts/personal/2024-04-08-prediction-of-feed-yields.md @@ -0,0 +1,123 @@ +--- +layout: post +title: "Predicting Feed Stream Yields in Gas Processing Plants Using Machine Learning" +date: 2024-04-08 +math: true +--- + +## Introduction + +This post is my initial attempt to apply AI and machine learning techniques to a challenge I often encounter in my professional environment. Due to confidentiality constraints, the data presented here is either synthetic or adjusted, but the methodology and modeling approaches remain valid for educational and demonstration purposes. + +Gas processing plants process and treat natural gas and its byproducts. They face operational challenges when feed compositions are unmetered or inaccurately estimated, especially when relying on outdated infrastructure or manual planning. The objective here is to predict product yields from various feed streams using machine learning methods like linear regression and neural networks. + +--- + +## Contributions + +- Developed ML models (linear regression, random forest, and neural networks) to predict feed yields. +- Applied these models to address real-world production planning challenges. +- Used correlation analysis and neural networks to extract nonlinear relationships between feeds and products. + +--- + +## Methodology + +To understand relationships between feed and product volumes, both visualization and correlation analysis were used. Outliers were removed using the Local Outlier Factor (LOF). We validated linearity with Pearson’s Correlation Coefficient and built neural networks initialized with linear regression weights for faster convergence. + +--- + +## Data Visualization and Exploration + +### Single-Feed Plants + +
+ Plant B + Plant K +
+ +### Multi-Feed Plants + +
+ Plant X + Plant Y +
+ +--- + +## Correlation Matrices + +**Plant B Correlation Matrix:** + +| | Feed B | C1 | NGL | +|----------|--------|--------|--------| +| Feed B | 1.00 | 0.95 | 0.67 | +| C1 | 0.95 | 1.00 | 0.67 | +| NGL | 0.67 | 0.67 | 1.00 | + +**Plant X Correlation Matrix (truncated):** + +| | Feed B | Feed S | Feed i | C1 | NGL | Sulphur | +|----------|--------|--------|--------|--------|--------|---------| +| Feed B | 1.00 | -0.21 | -0.37 | 0.17 | 0.26 | 0.21 | +| Feed S | -0.21 | 1.00 | -0.39 | 0.31 | -0.11 | 0.46 | +| Feed i | -0.37 | -0.39 | 1.00 | 0.09 | 0.30 | -0.28 | +| C1 | 0.17 | 0.31 | 0.09 | 1.00 | 0.35 | 0.68 | + +--- + +## Model Evaluation + +### Regression Performance (Plant X): + +| Model | R² | MSE | RMSE | MAE | CMAPE | +|----------------------|----------|----------|---------|---------|---------| +| Linear Regression | 0.305 | 137271 | 370.5 | 223.3 | 0.910 | +| Decision Tree | -0.092 | 178355 | 422.3 | 204.4 | 0.915 | +| Random Forest | 0.446 | 124168 | 352.4 | 186.1 | 0.929 | +| SVR | 0.036 | 217435 | 466.3 | 230.9 | 0.910 | + +### Regression Performance (Plant Y): + +| Model | R² | MSE | RMSE | MAE | CMAPE | +|----------------------|----------|----------|---------|---------|---------| +| Linear Regression | 0.403 | 377322 | 614.3 | 331.4 | 0.911 | +| Decision Tree | 0.350 | 374735 | 612.2 | 309.5 | 0.910 | +| Random Forest | 0.598 | 212575 | 461.1 | 229.4 | 0.931 | +| SVR | 0.062 | 830996 | 911.6 | 486.5 | 0.884 | + +--- + +## Neural Networks + +Neural networks improved fit quality significantly. Linear regression weights were used for initialization to improve convergence. + +
+ With vs Without Weight Init +
+ +**Best NN Evaluation (Plant Y, 5-fold cross-validation):** + +- **MSE:** 289,751 +- **CMAPE:** 91.16% +- **R²:** 0.989 + +--- + +## Yield Comparison + +| Feed | C1 (Emp) | NGL (Emp) | Sulphur (Emp) | C1 (NN) | NGL (NN) | Sulphur (NN) | +|------|----------|-----------|----------------|---------|----------|---------------| +| B | 0.72 | 7.80 | 1.55 | 1.18 | 9.74 | 2.69 | +| S | 0.84 | 2.00 | 2.00 | 0.12 | 9.35 | 0.17 | +| K | 0.70 | 9.47 | 0.00 | 0.14 | 3.10 | 0.00 | +| i | 0.84 | 2.49 | 0.90 | 0.42 | 3.86 | 1.43 | +| O | 0.50 | 23.40 | 1.90 | 0.98 | 12.18 | 2.12 | +| N | 0.80 | 6.67 | 0.60 | 1.75 | 10.45 | 1.42 | + +--- + +## Conclusion + +This study demonstrates how machine learning — especially neural networks — can improve yield estimation accuracy in gas processing. Even with limited features and noisy data, neural models outperformed traditional approaches. With better instrumentation or real-time data, these tools could become core to modern energy operations. + diff --git a/_posts/personal/2025-04-08-causal-policy-unemployment.md b/_posts/personal/2025-04-08-causal-policy-unemployment.md new file mode 100644 index 0000000000000..d37fe86ad4e45 --- /dev/null +++ b/_posts/personal/2025-04-08-causal-policy-unemployment.md @@ -0,0 +1,105 @@ +--- +layout: post +title: "Causal Effects of Monetary Policy on Unemployment: A Structural Approach" +date: 2025-04-08 +math: true +--- + +## Introduction + +As someone currently preparing for the **CFA exams**, I’ve been diving deeper into how macroeconomic policy impacts inflation, employment, and GDP. The curriculum often presents these causal relationships as established fact — but I became curious: **can we test these causal claims statistically?** + +This project is a personal attempt to bridge what I’m learning in economics from my CFA preparations using the tools of **causal inference** I learned in the Masters in Machine Learning. +In particular, I wanted to see whether Central Bank interest rate changes truly affect unemployment, and how we can model that effect using real-world data and tools like **do-calculus**. + +--- + +## Data Selection + +For this analysis, I used data from the [Federal Reserve Economic Data (FRED)](https://fred.stlouisfed.org/) due to its high-frequency monthly observations. Key indicators include: + +- **FEDFUNDS**: Federal Funds Rate +- **M2SL**: M2 Money Supply +- **CPIAUCSL**: Consumer Price Index (Urban, Seasonally Adjusted) +- **GDP Growth**: Real GDP % Change (Quarterly) +- **UNRATE**: Unemployment Rate + +To visualize assumed relationships between these variables, I started with a basic DAG inspired by standard macroeconomic models: + +![Causal DAG](/images/DAG cfa.png) + +--- + +## Data Preprocessing + +Since most variables are monthly except GDP (which is quarterly), I interpolated GDP values so each quarter value was copied across the respective three months. + +Exploratory time-series plots revealed correlations and suggested directions for further causal analysis: + +![Time Series Plot 1](/images/ts1.png) +![Time Series Plot 2](/images/ts2.png) + +--- + +## Granger Causality and DAG Adjustment + +To uncover temporal causality, I ran **Granger Causality** tests between variables. For instance: + +- GDP lag of ~3–5 months +- FEDFUNDS and M2 consistently Granger-caused inflation and GDP +- Bidirectional relationships between GDP and unemployment + +Based on these results, I updated the DAG: + +![Updated DAG](/images/DAG new.png) + +--- + +## Modeling the Effect of Interest Rate Intervention + +The key question: +What is the effect on **Unemployment** when the **Central Bank** changes interest rates? + +Formally: +\[ +P(\text{Unemployment\%} \mid do(\text{Fed Fund Rate})) +\] + +After applying **do-calculus**, the corresponding DAG is: + +![do-FED DAG](/images/DAG dofed.png) + +This isolates the intervention on interest rates from their usual causes (i.e., cutting all incoming arrows to FEDFUNDS). + +--- + +## Deriving the Interventional Distribution + +Using the adjusted DAG and applying rules of **do-calculus**, I arrived at: + +\[ +P(\text{Unemployment\%} \mid do(\text{Fed Fund Rate})) = +\sum_{\text{Inflation}, \text{M2}, \text{GDP}} +P(\text{Unemployment\%} \mid \text{M2}) +P(\text{M2} \mid \text{GDP}, \text{Inflation}) +P(\text{GDP} \mid \text{Fed Fund Rate}) +P(\text{Inflation} \mid \text{M2}) +\] + +Key reasoning: +- Conditioning M2 on GDP adjusts for confounders. +- Summing over GDP, Inflation, and M2 marginalizes confounding paths. +- The structure respects endogenous roles of variables like M2 and Inflation. + +--- + +## Next Steps + +I plan to estimate these conditional distributions using **Kernel Density Estimation (KDE)** to simulate: +\[ +P(\text{Unemployment\%} \mid do(\text{Fed Fund Rate})) +\] + +This will help visualize the shift in unemployment distribution resulting from monetary policy intervention. + +--- diff --git a/_sass/style.scss b/_sass/style.scss new file mode 100644 index 0000000000000..810c328b79079 --- /dev/null +++ b/_sass/style.scss @@ -0,0 +1,93 @@ +--- +# Only the main Sass file needs front matter (the dashes are enough) +--- + +@import + "minima/skins/{{ site.minima.skin | default: 'classic' }}", + "minima/initialize"; 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+ } + + .mobile-home-button a { + text-decoration: none; + color: #333; + } + + img { + max-width: 100%; + height: auto; + display: block; + margin: 0 auto; + } + + .btn, + .cv-button { + display: block; + margin: 1rem auto; + } + + blockquote { + margin-left: 0; + padding-left: 1rem; + border-left: 4px solid #aaa; + } +} + +/* 🖥️ Hide About Me post on desktop */ +@media screen and (min-width: 769px) { + .aboutme-mobile-only { + display: none !important; + } +} diff --git a/about.md b/about.md deleted file mode 100644 index bc21f5731bf4b..0000000000000 --- a/about.md +++ /dev/null @@ -1,15 +0,0 @@ ---- -layout: page -title: About -permalink: /about/ ---- - -Some information about you! - -### More Information - -A place to include any other types of information that you'd like to include about yourself. - -### Contact me - -[email@domain.com](mailto:email@domain.com) \ No newline at end of file diff --git a/assets/css/style.scss b/assets/css/style.scss new file mode 100644 index 0000000000000..810c328b79079 --- /dev/null +++ b/assets/css/style.scss @@ -0,0 +1,93 @@ +--- +# Only the main Sass file needs front matter (the dashes are enough) +--- + +@import + "minima/skins/{{ site.minima.skin | default: 'classic' }}", + "minima/initialize"; + +/* 🔽 Mobile-specific styling */ +@media screen and (max-width: 768px) { + .layout-wrapper { + flex-direction: column !important; + padding: 0 1rem; + } + + .sidebar, + .main-content, + .right-sidebar { + width: 100% !important; + padding: 0 !important; + margin-bottom: 1.5rem; + position: static !important; + } + + /* Sidebar: show icons only */ + .sidebar .label { + display: none !important; + } + + /* Post list appearance */ + .post-list li a { + display: block; + font-size: 0.9rem; + line-height: 1.3; + white-space: nowrap; + overflow: hidden; + text-overflow: ellipsis; + } + + .post-list li { + margin-bottom: 8px; + } + + /* About Me post - show only on mobile */ + .aboutme-mobile-only { + display: block; + } + + /* Mobile Home Button (top-left corner) */ + .mobile-home-button { + position: fixed; + top: 10px; + left: 10px; + background: #f5f5f5; + border: 1px solid #ddd; + border-radius: 8px; + padding: 6px 10px; + z-index: 1000; + font-size: 1.2rem; + box-shadow: 0 2px 5px rgba(0,0,0,0.1); 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- {% for post in site.posts %} - - {% endfor %} -
\ No newline at end of file diff --git a/index.md b/index.md new file mode 100644 index 0000000000000..a2d3148df69fe --- /dev/null +++ b/index.md @@ -0,0 +1,49 @@ +--- +layout: default +--- + +# Rames Nagib AlJneibi - رامس نجيب الجنيبي + +Welcome to my personal academic blog and portfolio. I’m currently pursuing a Master’s in Machine Learning and preparing for a PhD in Applied Mathematics. I’m passionate about uncovering deep structures in data and mathematics and applying them to real-world systems. + +I previously earned my Master’s in Mathematics and a Bachelor’s in Chemical Engineering. Professionally, I’ve worked across engineering, planning, and strategic roles in the Gas Business where I integrate technical expertise with long-term energy outlooks. + +## Research & Interests + +My academic and professional interests lie at the intersection of: + +- **Machine Learning & Time-Series Forecasting** +- **Optimization & Applied Mathematics** +- **Uncertainty Quantification and Conformal Prediction** +- **Energy Systems Planning & Gas Infrastructure** +- **Stochastic PDEs and Mathematical Modeling** + + +I’m currently focusing my Master’s thesis on **Conformal Prediction and Uncertainty Quantification**, while also exploring the intersection of **Numerical Methods for PDEs** and **Machine Learning**. + +My broader ambition is to contribute to the development of rigorous, real-world **mathematical models of physical systems**, bridging theory and application in meaningful ways. + +## Vision + +I believe that robust mathematical thinking is a superpower in today’s world — and I’m working toward becoming a **pioneer in data-driven decision-making** for energy and industrial systems. My goal is to lead impactful, intelligent solutions in one of the most critical sectors for global development. + +## Professional History + +- Senior Specialist – Gas Master Planning (Energy Sector) (2024-current) +- Senior Production Planning Engineer – ADNOC Gas (2022-2024) +- Process Engineer – ADNOC Refining (2019-2021) + +## Academic Journey + +While working full-time in a demanding technical and strategic role, I pursued my Master’s in Mathematics — and later began a second Master’s in Machine Learning. Despite the load of being a Full-Time student and Full-time Employee, I maintained strong academic performance while receiving promotions and high evaluations at work. That period tested and shaped my discipline, mental resilience, and passion for growth. + +It was during this time that I realized my ability to thrive at the intersection of theory and application — and it continues to fuel my vision for impactful, cross-disciplinary work. + + +## Personal Notes + +I’ve always loved helping others learn — whether as an older sibling, classroom tutor, or mentor — and I enjoy breaking down complex ideas into simple, digestible insights. + +My love for adventure and challenge extends beyond the academic realm. I’m into fitness and pursue my physical goals with the same discipline I apply to my intellectual ones. I primarily focus on bodybuilding, but I also enjoy long-distance running (even if I barely survive marathons) and challenging hikes that push my limits. + +There’s something deeply fulfilling about navigating both mind and body through effort and discomfort — and coming out stronger on the other side. diff --git a/style.scss b/style-backup.scss similarity index 100% rename from style.scss rename to style-backup.scss