I study how to learn from noisy, heavy-tailed data, and how to find signals that hold up out of sample. Across domains, my workflow is consistent: state the hypothesis before running the test, build the data from primary sources, validate with temporal splits, and stress-test every result before I rely on it.
A broker sits between a buyer and a seller, posts a price to each, and learns round by round what would have cleared. Most regret analyses of this problem assume valuations with bounded variance. I asked what happens when they have only a finite p-th moment for some p between 1 and 2, with no variance at all.
I characterized the minimax regret rate up to log factors, Õ(T(2−p)/p), achieved by truncated-mean estimation over epochs and matched by an Assouad lower bound, and carried it through to Hölder-smooth market values. The part I find most interesting is adaptivity. Under full feedback, a fully parameter-free median-of-means algorithm reaches the oracle rate for every p in (1, 2) at once, and extends to unknown smoothness through validation-based width selection. Not knowing the tail costs no polynomial factor, in contrast to heavy-tailed bandits.
The simulations bear this out. Without being told the tail index, the parameter-free algorithm finished with as little as 0.05× the regret of an oracle-tuned algorithm that knows the true tail parameters, on identical sample paths.
SEC Form 4 filings are public. When a corporate insider buys their own stock, it's a signal, and that much is well documented. I asked a sharper question: does the market's reaction at disclosure depend on where the stock sits when the purchase becomes public?
I built the dataset from raw Form 4 filings: 13,534 open-market purchases across 1,192 microcap issuers from 2018–2024, with split-adjusted prices, point-in-time share counts, and a fully reproducible pipeline in which every number in the paper is generated by code.
The answer is yes, and steeply. Purchases disclosed in the quintile farthest below the 52-week high earn a first-day abnormal return of 4.13%, against 0.86% for those nearest it (t = 9.77), while random days for the same companies show 0.14%. Scaled by each stock's own volatility, the reaction is still 2.5 times as large far below the high, a steeper gradient than for insider sales by the same issuers or for positive earnings surprises as a group, and the market absorbs it over two to three sessions.
The paper also shows how much a routine event-study choice matters: carrying the estimation-window intercept into the benchmark supplies 57% of the 30-day gradient measured under that benchmark.
This was my first research project, and it started with a practical problem: individual gene markers are unreliable across patient cohorts. A gene that performs well in one study often fails in another. I wanted to find features that were stable across populations.
I ran a random-effects meta-analysis across 6 independent gene-expression datasets. Individual gene expression levels were inconsistent, but certain ratios between genes held steady across all 6 cohorts. I built a composite ratio-based classifier on top of these stable features — it achieved an AUC of 0.92 with 85% sensitivity on independent validation, up from 0.52 using individual genes alone.
The lesson carried forward into everything I've done since: predictive power often lives in the relationships between features, not in any single feature on its own.