From a947cd05ff6458e1f00b1636538a4bafc7630d91 Mon Sep 17 00:00:00 2001 From: Oliver Date: Mon, 22 Mar 2021 00:20:35 -0400 Subject: [PATCH] Slides for Tuesday --- src/teaching/cse-562/2021sp/index.erb | 10 +- .../2021-03-23-ApproximateQueryProcessing.erb | 462 ++++++ .../2021sp/slide/2021-03-23/DBOJoin1.png | Bin 0 -> 85382 bytes .../2021sp/slide/2021-03-23/DBOJoin2.png | Bin 0 -> 72037 bytes .../slide/2021-03-23/DBOJoinOverview.png | Bin 0 -> 68607 bytes .../2021sp/slide/2021-03-23/IndexStriding.svg | 328 ++++ .../2021sp/slide/2021-03-23/JoinIssue-FKs.svg | 303 ++++ .../slide/2021-03-23/JoinIssue-Stratified.svg | 277 ++++ .../2021sp/slide/2021-03-23/JoinIssue.svg | 279 ++++ .../slide/2021-03-23/NaiveBootstrap.svg | 1269 ++++++++++++++++ .../slide/2021-03-23/NormalBootstrap.svg | 1327 +++++++++++++++++ .../slide/2021-03-23/OnlineAggregation.png | Bin 0 -> 2801 bytes .../2021sp/slide/2021-03-23/RippleJoin.svg | 301 ++++ 13 files changed, 4555 insertions(+), 1 deletion(-) create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23-ApproximateQueryProcessing.erb create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/DBOJoin1.png create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/DBOJoin2.png create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/DBOJoinOverview.png create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/IndexStriding.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/JoinIssue-FKs.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/JoinIssue-Stratified.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/JoinIssue.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/NaiveBootstrap.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/NormalBootstrap.svg create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/OnlineAggregation.png create mode 100644 src/teaching/cse-562/2021sp/slide/2021-03-23/RippleJoin.svg diff --git a/src/teaching/cse-562/2021sp/index.erb b/src/teaching/cse-562/2021sp/index.erb index 0361a68b..dc2481b8 100644 --- a/src/teaching/cse-562/2021sp/index.erb +++ b/src/teaching/cse-562/2021sp/index.erb @@ -54,6 +54,8 @@ schedule: materials: lecture: https://youtu.be/VGJMx1DZtK8 slides: slide/2021-03-04-Indexing2.html + bLSM_trees: "https://dl-acm-org.gate.lib.buffalo.edu/citation.cfm?id=2213862" + learned_indexes: "https://dl-acm-org.gate.lib.buffalo.edu/ft_gateway.cfm?id=3196909&type=pdf" - date: "Mar. 9" topic: "Cost-Based Optimization" materials: @@ -75,6 +77,12 @@ schedule: slides: slide/2021-03-18-ParallelQueries.html - date: "Mar. 23" topic: "Online Aggregation/Approximate Query Processing" + materials: + slides: slide/2021-03-23-ApproximateQueryProcessing.html + online_agg: https://dl-acm-org.gate.lib.buffalo.edu/doi/10.1145/253262.253291 + ripple_joins: https://dl-acm-org.gate.lib.buffalo.edu/doi/10.1145/304181.304208 + blinkdb: https://dl-acm-org.gate.lib.buffalo.edu/doi/10.14778/2367502.2367533 + other_readings: https://gitlab.odin.cse.buffalo.edu/odin-lab/documentation/-/wikis/ReadingList-Approximate-QPs - date: "Mar. 25" topic: "Streaming Queries" - date: "Mar. 30" @@ -179,7 +187,7 @@ In this course, you will learn...
<% if data.has_key? "due" %>Due: <%= data["due"] %>
<% end %> <%=data["topic"]%> - <% unless data.fetch("materials", {}).empty? %> ( <%= data["materials"].map { |r,url| "#{r}" }.join(" | ") %> )<% end %> + <% unless data.fetch("materials", {}).empty? %> ( <%= data["materials"].map { |r,url| "#{r.sub("_", " ")}" }.join(" | ") %> )<% end %> <% if data.has_key? "textbook" then %>
<%= data["textbook"] %>
<% end %> diff --git a/src/teaching/cse-562/2021sp/slide/2021-03-23-ApproximateQueryProcessing.erb b/src/teaching/cse-562/2021sp/slide/2021-03-23-ApproximateQueryProcessing.erb new file mode 100644 index 00000000..897b2385 --- /dev/null +++ b/src/teaching/cse-562/2021sp/slide/2021-03-23-ApproximateQueryProcessing.erb @@ -0,0 +1,462 @@ +--- +template: templates/cse4562_2021_slides.erb +title: OLA and AQP +date: March 23, 2021 +textbook: (readings only) +--- + +
+ + +
+

What is the best, correct technique for task X, when Y is true?

+
    +
  1. How do you define Correct and Best?
  2. +
  3. What correct alternatives are available?
  4. +
  5. How do you find the best available alternative
  6. +
+
+ +
+

So Far: Correct = The original RA for a query.

+

Only queries guaranteed to produce identical results are correct

+
+ +
+

What happens when Correct allows for a margin of error?

+
+ +
+
    +
  • Aggregate query with some margin of error.
  • +
  • ORDER BY LIMIT (Top-K) with some margin of error.
  • +
  • LIMIT without ORDER BY (Any-K).
  • +
+ +

Sacrifice a little accuracy for a lot of speed

+
+ +
+

Online Aggregation

+

Approximate Query Processing

+
+ +
+

+                        SELECT SUM(A) FROM R
+    
+ +

Naively, you need to see all values of R.A

+
+ +
+

Online Aggregation

+ +

$Avg(3,6,10,9,1,3,9,7,9,4,7,9,2,1,2,4,10,8,9,7) = 6$

+

$Avg(3,6,10,9,1) = 5.8$ $\approx 6$

+ +

$Sum\left(\frac{k}{N}\; Samples\right) \cdot \frac{N}{k} \approx Sum(*)$

+ +

Sampling lets you approximate aggregate values with orders of magnitude less data.

+
+ +
+ +
+ +
+

Question: How accurate is an estimate from $N$ samples

+
+ +
+

With $n$ tuples sampled uniformly with replacement

+ + + + + + + + + + + + + + +
$|AVG(samples) - AVG(real)|$The absolute error
$P(|AVG(samples) - AVG(real)| \geq \epsilon)$Its probability of exceeding error threshold $\epsilon$
$P(|AVG(samples) - AVG(real)| \geq \epsilon) \leq 2e^{\frac{2n\epsilon^2}{(max(real) - min(real))^2}}$... is below a threshold based on $\epsilon$, $n$, and the min/max value.
+

"Hoeffding's Bound"

+

See also "Chernoff's Bound" (similar) and "Serfling's Bound" (works without replacement).

+
+ +
+

What about non-sum-based aggregates?

+

Bootstrapping

+
+ +
+

Idea 1: Generate a bunch of samples of the same size and see how they're distributed.

+
+ +
+ +

The resulting histogram models the distribution of samples.

+
+ +
+

Problem: Generating samples is expensive!

+

Idea 2: Generate one sample, then resample to see how its distributed

+
+ +
+ +

The resulting histogram still models (in expectation) the distribution of samples.

+
+ +
+

Error Bounds

+
+
SUM, COUNT, AVG (sampling with replacement)
+
Hoeffding's Bound
+
Chernoff's Bound
+ +
SUM, COUNT, AVG (sampling without replacement)
+
Serfling's Bound
+ +
Any Other Aggregate
+
Bootstrapping
+
+
+
+ +
+
+ +

Keep adding samples until you reach a target accuracy

+

Keep adding samples until you run out of time

+
+ +
+

Generating Samples

+
+
+
Sampling From Disk
+
Random seeks are slow
+
+ +
+
Sampling For Group-By or Selections
+
Low-frequency events don't get sampled
+
+ +
+
Sampling From Joins
+
Fixing the Birthday Paradox
+
+
+
+ +
+ +
+
+

Sampling From Disk

+
+ +
+

Idea 1: Pick Randomly!

+ +

+      for i from 1 to num_samples:
+        sample_id = random(0, num_records)
+        samples += [ table.where( rowid = sample_id ) ]
+    
+
+ +
+ +
+ +
+

Problem: Random scans are EXPENSIVE.

+
+ +
+

Idea 2: Assume data already randomized!

+

Pick a random start record and read sequentially from there.

+
+ +
+ +
+ +
+

Problem: Sequential records are almost never IID.

+
+ +
+

Idea 3: Prebuild samples!

+

Shuffle data into fixed size sample buckets (e.g., BlinkDB).

+
+
+ +
+
+

Sampling From Group-By

+
+ +
+ + + + + + +
EmployeeCitySalary
AliceNYC$120k
BobNYC$110k
CarolNYC$115k
DaveSyracuse$80k
+

+      SELECT City, AVG(Salary) FROM NYS_Salaries;
+    
+
+ +
+

Problem: Most data is about NYC. With $N$ samples taken uniformly, margins of error for other cities are much bigger

+
+ +
+

Stratified Sampling

+

Generate $\frac{N}{\texttt{COUNT}(\texttt{DISTINCT } City)}$ samples for each group

+

Use $\texttt{COUNT}(\texttt{DISTINCT } City)$ instead of $\texttt{COUNT}(*)$ as the total group size

+
+ +
+

Index Striding

+
+ +
+ + "Online Aggregation" (Hellerstein et. al.) +
+ +
+

Idea 2: Pre-generate sample buckets across a range of different strata (e.g., BlinkDB).

+
+ +
+ +
+
+

Sampling from Joins

+
+ +
+ +
+ +
+

The Birthday Paradox

+ +

+ Assume: $\texttt{UNIQ}(A, R) = \texttt{UNIQ}(A, S) = N$ +

+ +

+ It takes $O(\sqrt{N})$ samples from both $R$ and $S$
to get even one match. +

+
+ +
+

Weighted Joins

+
+
Exploit Foreign Keys
+
Sample from the referencing table, join with full reference tables
+ +
Stratified Sampling
+
For many-many joins, stratify on the join attribute(s)
+
+
+ +
+

"Join Synopses"

+ +

$R \bowtie_B S \bowtie_C T$

+ +
    +
  • $R.B$ is a foreign key reference to $S.B$
  • +
  • $S.C$ is a foreign key reference to $T.C$
  • +
+ +

Sample from R, Use all of S, T

+
+ +
+

"Join Synopses"

+ + +
+ +
+

"Join Synopses"

+ +
    +
  • Foreign keys keep intermediate state small.
  • +
  • Fast evaluation with INLJ or In-Mem Hash Join.
  • +
  • Sampling is not biased.
  • +
+ + "Join synopses for approximate query answering" (Acharya et. al.) +
+ +
+

Stratified Sampling

+ + +
+ +
+

Stratified Sampling

+ +

For each tuple sampled from $R$, sample exactly one joining tuple from $S$

+ +
+ +
+ +

Question: Are we biasing the sampling process

+

Goal: Sample $r \bowtie s$ with probability $p((r\bowtie s) \in R\bowtie S)$

+

Actual: Sample $r \bowtie s$ with probability $p(r \in R) p((r\bowtie s) \in R\bowtie S | r \in R)$

+
+ +
+

Bayes' Theorem

+ +

+ $p(r \in R) p((r\bowtie s) \in R\bowtie S) | r \in R)$ + $= p(r \in R, (r\bowtie s) \in R\bowtie S)$ +

+

$\neq p((r\bowtie s) \in R\bowtie S)$

+ +
+ +
+

Corrective Factor

+ +

+ $p(r \in R, (r\bowtie s) \in R\bowtie S)$ + $\cdot n$ + $= p((r\bowtie s) \in R\bowtie S)$ +

+ +

+ $n = \frac{ p((r\bowtie s) \in R\bowtie S) }{ p(r \in R, (r\bowtie s) \in R\bowtie S) }$ +

+

+ $ = \frac{ 1 }{ p(r \in R | (r\bowtie s) \in R\bowtie S) } $ + $\approx |R| \cdot |\{\;s\;|s \in S, r.A = S.A\;\}$ +

+

The probability that a tuple in $R$ participates in a join.

+

+
+ +
+

Should I sample from $R$ or $S$ first?

+

(What if only one tuple from $R$ joins with every tuple from $S$)

+
+ +
+

"Wander Join"

+ +

Sample with all join orders at random.

+ + + "Wander Join: Online Aggregation via Random Walks" (Li et. al.) + +
+ + +
+ +
+
+

Convergent Joins

+
+
Ripple Join
+
Incrementally increase the sample size
+ +
Turbo DBO Join
+
Re-use data loading to get "lucky" joins
+
+
+ +
+

Idea 1: Start small, keep making the sample size bigger

+
+ +
+

Ripple Join

+ $$Q = R \bowtie S$$ +
    +
  1. $Q \leftarrow \emptyset$, $R_{sample} \leftarrow \emptyset$, and $S_{sample} \leftarrow \emptyset$
  2. +
  3. Sample $r \in R$
  4. +
      +
    1. $Q \leftarrow r \bowtie S_{sample}$
    2. +
    3. $R_{sample} \leftarrow R_{sample} \uplus \{r\}$
    4. +
    +
  5. Sample $s \in S$
  6. +
      +
    1. $Q \leftarrow s \bowtie R_{sample}$
    2. +
    3. $S_{sample} \leftarrow S_{sample} \uplus \{s\}$
    4. +
    +
  7. Goto 2
  8. +
+
+ +
+

Ripple Join

+ +
+ +
+

Idea 2: Normal BNLJ, but piggyback sampling off of the results.

+
+ +
+ +
+ +
+ +
+ +
+ +
+ + + +
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