CS451: Data-Intensive Distributed Computing

https://student.cs.uwaterloo.ca/~cs451/syllabus.html

~~Really great teacher~~. Has gone downhill as the term progressed. Became boring. Though slides are pretty good.

Things to master for final:

LSH-hashing
DStream??
Syntax for Spark (things like reducebykey, tf does that do?)
Bigram frequency, boolean retrieval, page rank, how the logic is actually implemented?? cuz i forgot

Concepts

A3:

Need to get an more efficient reducer? Like doing (A,B): C instead of A: (B,C)?
- But aggregating the counts seems like a pain. It’s like doing pairs instead of stripes

Running the reference checks

hadoop jar target/assignments-1.0.jar ca.uwaterloo.cs451.a3.BuildInvertedIndex \
   -input data/Shakespeare.txt -output cs451-s36gong-a3-index-shakespeare

Query

hadoop jar target/assignments-1.0.jar ca.uwaterloo.cs451.a3.BooleanRetrieval \
   -index cs451-s36gong-a3-index-shakespeare -collection data/Shakespeare.txt \
   -query "outrageous fortune AND"
   
hadoop jar target/assignments-1.0.jar ca.uwaterloo.cs451.a3.BooleanRetrieval \
   -index cs451-s36gong-a3-index-shakespeare -collection data/Shakespeare.txt \
   -query "white red OR rose AND pluck AND"

First output

Query: outrageous fortune AND
1073319     The slings and arrows of outrageous fortune

Second output

Query: white red OR rose AND pluck AND
1713274     From off this brier pluck a white rose with me.
1713428     Pluck a red rose from off this thorn with me.
1713566     I pluck this white rose with Plantagenet.
1713612   SUFFOLK. I pluck this red rose with young Somerset,
1714623     In sign whereof I pluck a white rose too.

Chapter 2 and 3

Those notes are in MapReduce, RDD and Spark.

Chapter 4: Dealing with Text

The goal is to generate text. We can use a probabilistic model.

P(“I saw a van”) = P(“I”) x P(“saw” | “I”) x P(“a” | “I saw”) x P(“van” | “I saw a”)

But how feasible is this?

Not really. We use a smaller limit: the n-gram
Limit of $n$ words

Basic Idea: Probability of next word only depends on the previous (N – 1) words

$P (w_{k} ∣ w_{1}, w_{2}, \dots w_{k - 1}) \approx P (w_{k} ∣ w_{k - N + 1}, w_{k - N + 2}, \dots, w_{k - 1})$

N = 1 : Unigram Model- P(w1 ,w2 ,w3 ,…) = P(w1 ) P(w2 ) … P(wk )
N = 2 : Bigram Model - $P (w 1, w 2, w 3, \dots) = P (w 1) P (w 2∣ w 1) \dots P (w k ∣ w k - 1)$

State of the art rarely goes above 5-gram.

We apply laplace smoothing for the bigram probabilities.

A posting consists of a record that associates a specific word (or term) with a set of documents in which that word appears.

Terminology:

Inverted Index. Maps context to documents.
Forward Index. Maps documents to context. (Seems strange to me, so a book’s index is “inverted”?)
so the word is simply a mapped to in which document it is in

Postings size use Zipf’s Law: $f (k; s, N) = \frac{1}{\sum _{n = 1}^{N} ( 1/ n ^{s} )}$

$N$ is the number of elements
$k$ is the rank, anywhere between $1$ and $N$
$s$ is the characteristic exponent

Zipf’s Law: (also) linear in log-log space

A few elements occur very frequently
Many elements occur very infrequently
Ohh, it’s like the 80-20 Rule - https://www.youtube.com/watch?v=fCn8zs912OE&t=253s&ab_channel=Vsauce

Instead of using that structure, use a linked list!!

Boolean Retrieval

Hits: Set of documents for which the query is true

Ranked retrieval is introduced.

The relevance of a document is the sum of the wi value

Chapter 5: Graphs

How do we do mapreduce on graphs?

See

Data Mining: Part 1

A/B testing for ML: Step 1: Offline training and evaluation (holdout, cross-validate, etc) Step 2: A/B testing vs other methods

Data Mining: Part 2

Problem:

S – Set of Objects
D(a,b) – Distance from object a to b
t – maximum distance threshold

Goal: Find all unordered pairs (a,b) s.t. D(a,b) ≤ t

Find the top 42 matching images, and then fill it in

Capturing similarity is difficult

Images
Protein
Text

Given high-dimensional datapoints $x_{1}, x_{2}, \dots x_{n}$ and some distance function $d (x_{1}, x_{2})$ : Find all pairs of datapoints $x_{i}, x_{j}$ s.t. $d (x_{i}, x_{j}) < s$

The naïve approach: just compute $d (x_{i}, x_{j})$ for all $i, j$ $O (n^{2})$ – not very big data Magic: $O (n)$ – normal to want, and possible to achieve.

Use LSH

Why do we care? The core technique applies to ML!

(Scalar) LSH to find Near Neighbours

Make a Hash Table
Use buckets that are $w$ wide (and overlapped, so items go in multiple buckets)
Most values $x_{i}, x_{j}$ s.t. $d (x_{i}, x_{j})$ < c will have at least 1 bucket in common
Most values > c will NOT share a common bucket

• Sets as vectors: Measure similarity by the cosine distance • Sets as sets: Measure similarity by the Jaccard distance • Sets as points: Measure similarity by Euclidean distance

Part 2 of data mining

Measuring distance between text documents: Remember, one goal is detecting duplicate news stories

Diff: Too sensitive to rearrangement
Word Count / Bag of Words: not sensitive enough to rearrangement
Edit Distance: too difficult to compute
doc2vec cosine distance: (too advanced)
N-Grams: Just right

Jaccard How do n-grams give us a distance measure? Jaccard distance! This is used for sets.

Do we have sets? Yes: A document embedding is the set of n-grams it contains.

Here’s how we compute the similarity metric:

$s im (C 1, C 2) = \frac{C 1 \cap C 2}{∣ C 1 \cup C 2∣}$

These are the distances $d (C 1, C 2) = 1 - s im (C 1, C 2)$

What $n$ to use?

What n should I use?

There’s a few factors:

Depends on if you’re doing byte-level or word-level n-grams

Depends on what size of documents

For byte-level:

4-5 for short documents (tweets, sms, emails)

8-10 for long documents (webpages, books, papers)

For word-level:

2-3 for short documents

3-5 for long documents

Min-Hashing

Chapter 7: Relational Data

This is a cool diagram that the teacher showed
https://www.reddit.com/r/ProgrammerHumor/comments/y3ykga/database_alignment_chart/

Database Workloads OLTP (Online Transaction Processing)

Most Applications:
- E-Commerce, Banking, Reddit, etc.
User Facing: Must be fast, low latency, concurrent (many users)
Tasks: small set of common queries
Access: Random reads, small writes

OLAP (Online Analytical Processing)

BI and Data Mining
Back-End: Batch workloads, low concurrency
Tasks: Complex Analytics (Ad Hoc)
Access: Full Table Scans, Big Data

Two patterns, one database

To satisfy both needs, we use a data warehouse

So how do we do all these operations in mapreduce?

UNION → Hadoop MapReduce has a MultipleInputFile class

SUBSTRACT

MultipleInputFiles again – Each mapper has:
- Key: An Entire Tuple, plus “Which Mapper Sent Me”
- Value: Not used
- Sort “RHS” tuples before equal “LHS” tuples
Reducer
- Remember last RHS tuple
- Emit LHS tuples only if they do not equal the last RHS

CROSS PRODUCT

NO, GOD NO

Inner joins

Chapter 10: Mutable State

https://student.cs.uwaterloo.ca/~cs451/slides/09%20-%20Mutable%20State%20-%20Combined.pdf

Chapter 9

Bloom Filter

🛠️ Steven Gong

Table of Contents

CS451: Data-Intensive Distributed Computing

Chapter 2 and 3

Chapter 4: Dealing with Text

Boolean Retrieval

Chapter 5: Graphs

Data Mining: Part 1

Data Mining: Part 2

Part 2 of data mining

Chapter 7: Relational Data

Chapter 10: Mutable State

Chapter 9

Graph View

Backlinks