Projects & Portfolio

This project tackles a critical and notoriously difficult problem in time-series analysis: learning true causal structures when data is measured much slower than the true underlying process (i.e., "undersampling"). This mismatch is common in fields like neuroscience—where fMRI scans are far slower than neural activity—and leads to standard causal learning methods producing misleading results.

The core innovation of this work is a new algorithm, sRASL (Solver-based Rate-Agnostic Structure Learning), which finds the true, fast-timescale causal graph without knowing the undersampling rate. This was achieved by skillfully reformulating the (NP-complete) search problem into a highly efficient constraint satisfaction problem. This approach demonstrates a strong command of Answer Set Programming (ASP), a sophisticated declarative logic framework used to solve complex combinatorial problems.

The project's mathematical rigor is showcased in two key areas:

• Novel Constraints: The algorithm's speed does not come from a simple translation to ASP. It integrates novel theoretical insights, introducing new constraints based on the graph-theoretic properties of Strongly Connected Components (SCCs). This innovation prunes the search space exponentially, enabling massive performance gains.
• Formal Guarantees: The method was formally proven to be correct and complete by showing it is a "direct encoding" of the undersampling problem, guaranteeing it finds the entire set of valid solutions.

Finally, the algorithm includes a robust optimization mode that handles real-world statistical noise, allowing it to find the 'closest' valid causal graph even when the input data is imperfect.

The results were a breakthrough in scalability, demonstrating:

• Speed: A speed-up of over three orders of magnitude (e.g., reducing a benchmark from ~1000 minutes to 6 seconds).
• Scale: The ability to analyze graphs with over 100 nodes, a massive leap from the previous 6-node limit.

This research challenges a fundamental assumption in data-driven science. The common belief is that to improve causal discovery, one must always measure a system faster. Our innovation was to formally prove this is incorrect: we show that new information can be gained by deliberately adding a slower measurement. This counter-intuitive "non-monotonic undersampling" phenomenon works because the slower timescale provides a different "perspective" on the system, helping to eliminate "causal illusions" (ambiguities) that exist at a single timescale.

To operationalize this discovery, this project introduced the dRASL algorithm. This demonstrates advanced skills in Answer Set Programming (ASP), as dRASL is a novel generalization of our previous sRASL solver. Instead of just solving for one observed graph, dRASL is designed to find the joint equivalence class of causal structures consistent with multiple graphs from different timescales (e.g., H_u and H_v).

The mathematical rigor of this work is grounded in the formal conditions for non-monotonicity. We performed extensive computational experiments to validate the theory. The key results are:

• It Works: We proved the phenomenon exists. In one example, adding a slower graph (G₅) to an existing one (G₄) reduced the equivalence class (the number of possible solutions) from 11 graphs to 3.
• It's Common: This benefit is not a rare edge case. We found it occurs most frequently in sparse causal graphs—a property that aligns with the density of many real-world systems, such as brain or social networks.
• It's Powerful: The "gain" from this method is significant, commonly reducing the solution space by 1-2 orders of magnitude (10x-100x), with some cases showing a 1000-fold reduction.

This research provides a new, low-cost path for improving causal discovery and shows that historical, slower-timescale data can be reused to gain new insights.

Greedy AutoAugment: Efficient Data Augmentation Search

This project tackles a major bottleneck in modern deep learning: the extreme computational cost of finding optimal data augmentation policies. While AutoAugment proved that learning policies from data leads to state-of-the-art results, its reliance on a complex Reinforcement Learning (RL) controller to search an exponential search space makes it impractically expensive. This forces most researchers to re-use pre-trained policies on new datasets, which, as this paper shows, can actually hurt performance.

Our Greedy AutoAugment (GAutoAugment) is an innovative solution that replaces this "black-box" RL approach with a highly efficient, transparent, and more effective search algorithm. This work demonstrates deep skills in algorithmic design, computational optimization, and complexity analysis.

Innovation and Mathematical Rigor

The core innovation is a greedy, layer-by-layer search that transforms the problem's complexity.

• Algorithmic Redesign: We replaced the slow RL controller with a Greedy Breadth-First Search. The algorithm iteratively builds policies, starting with a single augmentation (layer 1) and evaluating all combinations. It then greedily selects the best-performing policy from that layer to serve as the base for the next layer of the search.
• Search Space Transformation: The key mathematical insight was to decouple the search variables. Instead of searching for (technique, probability, and magnitude) simultaneously, we fixed the probability to 1 during the search. This single design choice, combined with the greedy search, fundamentally changed the computational complexity from an exponential growth (O(N^l)) to a linear growth (O(N×k)).
• Statistical Re-weighting: After the highly efficient search identifies the best policies, we re-introduce probabilities in a statistically sound manner. We use a Pareto distribution to assign higher selection probabilities to the policies that achieved higher accuracy during the search. This ensures that better policies are used more often during the final model training.

Key Results

This algorithmic and mathematical rigor directly translated into superior performance.

• Massive Efficiency: GAutoAugment finds better policies while using 360 times fewer computational resources than the original AutoAugment.
• Superior Accuracy: By being efficient enough to find dataset-specific policies, GAutoAugment consistently improved accuracy across four datasets (Tiny ImageNet, CIFAR-10, CIFAR-100, and SVHN) and 11 different neural network architectures.
• Solved Transferability: We demonstrated that transferring policies is sub-optimal. The "one-size-fits-all" AutoAugment policy decreased accuracy on Tiny ImageNet by 52% compared to manual augmentation, while our dataset-specific search increased accuracy by 25%.

During the COVID-19 pandemic, healthcare systems faced two critical bottlenecks: a shortage of diagnostic tests and a shortage of expert radiologists to interpret CT scans. This project tackled both problems by developing a novel deep learning architecture, DECAPS (Detail-Oriented Capsule Networks), designed to automate COVID-19 diagnosis from CT scans with superhuman accuracy, even when trained on scarce data.

This work demonstrates advanced skills in algorithmic design, generative modeling, and deep learning theory. Our innovations were:

Novel Architecture (DECAPS): We didn't just use a standard CNN. We built our solution on Capsule Networks to better model the part-whole spatial relationships in a CT scan. We fundamentally improved the architecture by introducing:

• Inverted Dynamic Routing (IDR): A new, top-down routing mechanism that forces lower-level capsules to compete for the attention of higher-level ones. This rigorously-designed algorithm proved more stable and was crucial for filtering out noise from non-descriptive regions of the lung.
• "Peekaboo" Training: A novel, self-guided training procedure. The model uses its own activation maps to identify a region of interest (ROI). It then crops the ROI to force the network to learn fine-grained details, and drops (removes) the ROI to force the network to find all relevant disease features, not just the most obvious one.
• Generative Data Augmentation: To solve the critical "data scarcity" problem, we employed conditional Generative Adversarial Networks (cGANs). We used a pix2pix model to learn the distribution of COVID-19 features and generate hundreds of realistic, synthetic CT scan "deep fakes," which were vetted by our collaborating radiologists.

Key Results

Our approach was a resounding success, demonstrating a clear path to augmenting clinical experts.

• State-of-the-Art Performance: The final DECAPS model achieved 96.1% AUC, significantly outperforming standard, powerful architectures like ResNet50, Inception-v3, and DenseNet121.
• Superhuman Accuracy: The model was benchmarked against three experienced, well-trained thoracic radiologists. On a high-quality, curated test set, DECAPS significantly outperformed all three human experts, achieving 98% AUC.
• Interpretable & Collaborative: The model generates Head Activation Maps (HAMs) to visualize exactly what regions it used to make its diagnosis. The clinical utility was so high that in one case, a radiologist revised their initial diagnosis after seeing the features our AI had highlighted.

"Piecing Together the Causal Puzzle" confronts one of neuroimaging's toughest challenges—recovering the true causal structure from undersampled, noisy time series data. This work innovates by leveraging Answer Set Programming (ASP) to rigorously explore and prune the space of potential causal graphs.

Demonstrates robust performance on simulated fMRI data, accurately preserving the BOLD signal across varying undersampling rates.

This project introduces ION-C, a computationally efficient algorithm that builds a single, unified causal model from separate, partially overlapping datasets. We solved a major scalability problem with the original "ION" algorithm, which was unusable on graphs with more than 6 nodes

Our key achievement was reformulating the problem using Answer Set Programming (ASP), creating a new method that is provably sound and complete. We successfully scaled this new algorithm to graphs with up to 25 nodes.

Simulation results showed extremely high accuracy: causal links that appeared in ≥90% of solutions were 99.55% accurate to the ground truth. We also demonstrated a real-world application on European Social Survey data, where ION-C successfully identified a plausible causal connection between two variables that were never measured together in the same survey.

Worked on integrating Llama 3 with knowledge graphs to improve logical reasoning and problem-solving in AI models. This project explores how structured knowledge can enhance the reasoning capabilities of large language models for complex problem-solving tasks.

Trained GANs to augment and improve the classification of street signs under diverse weather conditions using multimodal inputs (image & text). This approach enhances the robustness of autonomous vehicle perception systems.

Developed a contrastive learning framework with a topology loss term to reduce texture bias in CNNs, improving generalization in vision tasks. This method encourages networks to learn more robust shape-based representations.

Built neural networks (PhICNet) to predict physical systems governed by PDEs, integrating multimodal physics and image data for enhanced spatio-temporal forecasting. This approach combines physics-informed learning with computer vision.

Designed an eye-tracking device from scratch using C#.NET, OpenCV, Emgu, and AForge libraries. Achieved high-accuracy gaze detection for real-time applications including assistive technology and human-computer interaction.