How much of your privacy budget is left after ten queries?
A privacy guarantee applies to the whole sequence of queries, not to each query in isolation.
Technical notes
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AI, analytics, and systems explained from first principles—with derivations you can open and parameters you can move.
20 notes across 14 subjects, 17 of them with interactive figures.Collections
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Energy Analytics
Start with “A 100 MW plant rarely delivers 100 MW”
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Retail Analytics
Start with “Confidence lies about which products sell each other”
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Azure AI Architecture
Start with “Before you build an agent, decide whether you should”
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Retail Analytics
Start with “Confidence lies about which products sell each other”
3 notes · Collection
Azure AI Architecture
Start with “Before you build an agent, decide whether you should”
Featured explorable
How much of your privacy budget is left after ten queries?
A privacy guarantee applies to the whole sequence of queries, not to each query in isolation.
A single differentially private query can be both accurate and private. Run many against a fixed privacy budget and the noise each one needs grows with every question asked — the mistake that turns a well-designed privacy mechanism into a useless one.
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Curated from first principles to field notes
Before you build an agent, decide whether you should
Choose the least autonomous architecture that can complete the job reliably.
Microsoft Foundry is one platform pretending to be three products
Microsoft Foundry joins model, agent, tool, and evaluation work around shared project resources.
Copilot Studio didn't need a new protocol until agents had to talk to each other
MCP connects an orchestrator to tools; A2A coordinates agents across a separate trust boundary.
Betweenness and degree can crown different nodes on the same graph
The most important node changes when the question changes from reach to brokerage.
The same five numbers, three axis floors, three different stories
Changing an axis floor changes perceived movement even when every data value stays fixed.
A better fit on your training data can predict worse
Lower training error can mean worse unseen predictions when extra flexibility starts fitting noise.
Ridge shrinks the directions your data trusts least
Ridge shrinks coefficients most along directions the observed data identifies least reliably.
A sigmoid's gradient tops out at 0.25 — that's the vanishing-gradient problem
Chaining sigmoid derivatives no larger than 0.25 can shrink a deep gradient exponentially.
What happens to the patients still alive when a trial ends?
A censored patient still contributes survival information until the moment they leave observation.
Can a treatment win in every subgroup and still lose overall?
Unequal subgroup weights can reverse an aggregate comparison even when every subgroup agrees.
Does adding more assets actually diversify a portfolio?
Diversification depends on covariance between assets, not on the number of assets alone.
What a shadow price actually tells you (and where it stops being true)
A shadow price is a local marginal value that holds only while the active constraints stay unchanged.
Pooling warehouses can halve your safety stock — if demand actually cooperates
The square-root pooling benefit assumes independent demand; positive correlation erodes it.
1.18× is the arbitrage floor a battery actually needs
A battery breaks even on energy only when the high price exceeds the low price divided by efficiency.
A 100 MW plant rarely delivers 100 MW
Capacity factor converts a plant’s nameplate rating into the energy it actually produces over time.
Solar can push the electricity price to zero — and that's a problem
In a marginal-price market, enough zero-cost supply drives the clearing price down to the lowest offer in the stack.
Confidence lies about which products sell each other
Confidence ignores how common the consequent already is; lift compares against that baseline.
Price sensitivity alone sets your optimal markup
Under the stated demand assumptions, the optimal markup is pinned down by elasticity.
Targeting your likeliest buyers wastes most of your promo budget
Promotion targeting should rank incremental responders, not customers already likely to buy.
How these are written
Every note states its assumptions, shows the derivation rather than asserting the result, and ends with the failure modes. Where a parameter matters, you can move it and watch what happens. Where recall matters more than reading, the answer is hidden until you have tried.