- Tons of Curation Heuristics Available!
+We have tools that can solve these problem!
- 
- ... that can be wrong
+... most of the time
- ... very wrong
-+ Problem: It's hard to trust tools that can be wrong! +
+Options
+-
+
- Ignore the Problem + + +
- In the name of Codd,
thou shalt not give the user a wrong answer.
-
+
+
+ In the name of Codd
Thou shalt not give the user a wrong answer.
+
... but when combined with heuristics
Options
+-
+
- Ignore the Problem +
- Heresy + +
On representing incomplete information in a relational data base
-T. Imielinski & W. Lipski Jr.(VLDB 1981)
-
- Incomplete and Probabilistic Databases
have existed since the 1980s...
-
T. Imielinski & W. Lipski Jr.(VLDB 1981)
- (Typical Heuristics)
+ +1. ProbDBs Produce Probability Distributions as Outputs
+2. ProbDBs Require Probability Distributions as Inputs
- (Probabilistic Query Outputs)
-Probabilistic Databases...
-
-
- ... require probabilities as inputs -
- ... are slow -
- ... produce probabilities as outputs +
- ... require probabilities as inputs +
- ... produce probabilities as outputs +
- ... are slow +
Options
+-
+
- Ignore the Problem +
- Heresy +
- ?
-
-
- Why should you care about uncertain data? -
- Background: K-Relations and Possible Worlds -
- Uncertainty-Annotated Databases(Joint work with Boris Glavic, Su Feng, Aaron Huber)
-
- Other Mimir Projects -
Uncertainty-Annotated Databases
+(Joint work with Boris Glavic, Su Feng, Aaron Huber)
+Other Projects
+-
+
- Adaptive Schemas +
- Probabilistic Query Compilers +
-
-
- Semirings -
- K-Relations +
- Possible Worlds -
- Certain, Possible Tuples -
Background
+ +$K$-Semirings
+
|
+ + |
|
+
The relational view
+The functional view
++ $$R(1, 2) \mapsto 1$$ + $$R(1, 3) \mapsto 1$$ + $$R(4, 3) \mapsto 1$$ +
++ $$R(4, 5) \mapsto 0$$ +
++ $$S(3, 6) \mapsto 2$$ +
+$= S(3, 6) + S(3, 6)$
+$= 2 + 2 = 4$
+$= R(4, 3) \times S(3, 6)$
+$= 1 \times 2 = 2$
+$= \sum_{Y} R(Y, 3)$
+$ = R(1, 3) + R(4, 3) + \ldots$
+$= 1 + 1 + 0 = 2$
+| $\cup$ | $\approx$ | $+$ |
| $\bowtie$ | $\approx$ | $\times$ |
| $\pi$ | $\approx$ | $+$ |
Provenance Semirings
+T.J. Green & G. Karvounarakis & V. Tannen(PODS 2007)
+| Semiring | Equivalent Query Semantics | +
|---|---|
| $\left<\mathbb N, +, \times, 0, 1\right>$ | +Bag Semantics | +
| $\left<\mathbb B, \vee, \wedge, \bot, \top\right>$ | +Set Semantics | +
| $\left<\mathcal K^W, \vec \oplus, \vec \otimes, \mathbb{\vec 0}, \mathbb{\vec 1}\right>$ | +Possible Worlds Semantics | +
-
-
- $K^W$-Relations -
- $PW_i$, Certain, Possible -
- Performance -
$K^W$-Semirings
+| R | A | B |
|---|---|---|
| 1 | 2 | |
| 1 | 3 | |
 | 3 |
|
+ + |
|
+
| R | A | B | |
|---|---|---|---|
| 1 | 2 | $\mapsto [1,1]$ | |
| 1 | 3 | $\mapsto [1,1]$ | |
| 4 | 3 | $\mapsto [1,0]$ | |
| 9 | 3 | $\mapsto [0,1]$ |
Extractors
+ + $$\mathcal K^W \rightarrow \mathcal K$$ + (plug in any $K$-Semiring-compatible $\mathcal K$) + +-
+
- Possible World Value +
- $\texttt{PW_i}(\vec k) \equiv \vec k_i$ +
- Certain Value +
- $\mathcal C(\vec k) \equiv min(\vec k)$ +
- Possible Value +
- $\mathcal P(\vec k) \equiv max(\vec k)$ +
+
|
+
+ $$\texttt{PW}_0(R(1, 2)) = 1$$ +$$\texttt{PW}_0(R(4, 3)) = 1$$ +$$\texttt{PW}_1(R(4, 3)) = 0$$ +$$\mathcal C(R(4, 3)) = 0$$ +$$\mathcal P(R(4, 3)) = 1$$ + |
+
Thanks...
+ +A quick step back into reality...
+
+ 
+
+ | R | A | B |
|---|---|---|
| 1 | 2 | |
| 1 | 3 | |
| 4 or 9 | 3 |
+
| R | A | B |
|---|---|---|
| 1 | 2 | |
| 1 | 3 | |
| 4 or 9 | 3 |
Standard practice: "Just use the best option."
+
+ What's in between these extremes?
+| R | A | B | |
|---|---|---|---|
| 1 | 2 | ||
| 1 | 3 | ||
| 4 | 3 | * |
+ Use the best option, but mark potential errors.
+| $PW_{i}(Q(\mathcal D))$ | +The results Alice would have "just used". | +
| $\mathcal C(Q(\mathcal D))$ | +Which of those results are trustworthy. | +
(Computing $PW_{i}(Q(\mathcal D))$ is cheap!)
+Can we do the same thing for $\mathcal C(Q(\mathcal D))$?
+No.
+| R | A | B | $K^W$ | $\mathcal C$ | |
|---|---|---|---|---|---|
| 1 | 2 | $\mapsto$ | $[1,1]$ | 1 | |
| 1 | 3 | $\mapsto$ | $[1,1]$ | 1 | |
| 4 | 3 | $\mapsto$ | $[1,0]$ | 0 | |
| 9 | 3 | $\mapsto$ | $[0,1]$ | 0 |
Compute $\pi_B(R)$
+| $\pi_B$R | B | $K^W$ | $\mathcal C$ | |
|---|---|---|---|---|
| 2 | $\mapsto$ | $[1,1]$ | $1$ | |
| 3 | $\mapsto$ | $[2,2]$ | $1+0+0=1$ |
So what can we do with $\mathcal C$?
+We can Approximate
+-
+
- Soundness +
- $Q(\mathcal C(\mathcal D)) \leq \mathcal C(Q(\mathcal D))$ +
- We can efficiently compute a conservative approximation of $\mathcal C$. + +
- Completeness +
- $Q(\mathcal C(\mathcal D)) = \mathcal C(Q(\mathcal D))$ ...if $Q$ is safe +
... also attribute level uncertainty
+Defining Possible Worlds
+Mimir allows users to define special UDFs called Models.
+
+ CREATE MODEL TYPE Geocoder AS mimir.models.GeocodingModel;
+
+ CREATE MODEL INSTANCE Text_To_Loc USING Geocoder('Google');
+
+ SELECT C.name, C.id, Text_To_Loc(C.address) AS address
+ FROM Customer C;
+ (Not actual Mimir-SQL. Language adapted for your viewing pleasure.)
+Models...
... return one best guess
... define the space of alternatives
Example Models
+ +-
+
- Geocoding Addresses +
- Imputation using a SparkML classifier +
- Heuristic detection of order-by columns for interpolation +
- Schema matching based on edit-distance +
- MayBMS-style probabilistic repair-key +
- And more... +
Convenience Operators: Lenses
+ +Lenses instantiate/train a model and wrap a query
+-
+
- Domain Constraint Repair / Missing Value Imputation +
- Schema Matching +
- Sequence Repair +
- Key Repair +
- Arbitrary Choice +
- Type Detection * +
- Header Detection * +
- JSON Shredder * +
Evaluation handled by a DBMS or Spark via query rewriting.
+
+ SELECT C.name, C.id, Text_To_Loc(C.address) AS address
+ FROM Customer C;
+ becomes...
+
+ SELECT C.name, C.id, Text_To_Loc(C.address) AS address,
+ 1 AS name_certain, 1 AS id_certain,
+ 0 AS address_certain, 1 AS row_certain
+ FROM Customer C;
+ A few more things we're doing with Mimir...
+Adaptive Schemas
+ +-
+
- Domain Constraint Repair / Missing Value Imputation +
- Schema Matching +
- Sequence Repair +
- Key Repair +
- Arbitrary Choice +
- Type Detection * +
- Header Detection * +
- JSON Shredder * +
Adaptive Schemas
+ +-
+
- Domain Constraint Repair / Missing Value Imputation +
- Schema Matching +
- Sequence Repair +
- Key Repair +
- Arbitrary Choice +
- Type Detection * +
- Header Detection * +
- JSON Shredder * +
+ LOAD 'customers.csv';
+
+ SELECT name FROM customers WHERE last_purchase < LAST_WEEK();
+ How does the system know...
+-
+
- ... which column is 'name'? +
- Guess that row 1 is headers. + +
- ... that 'last_purchase' is a date? +
- All rows look like YYYY-MM-DD +
This is all guesswork!
+Idea: Make the System Catalog a Probabilistic Table
+Probabilistic Query Compilers
+Sampling from ProbDBs is Sloooow
+Trivial Sampling
+Evaluate the query $N$ times.
Plug in samples instead of best guesses.
Better Solutions
+Merge evaluation to mitigate redundancy.
+Sparse Encoding
+
+
| + âž” + |
+
|
Tuple Bundles
+
+
| + âž” + |
+
|
Idea: Let the compiler pick the right representation
(or combination)
| Students | @@ -364,21 +944,21 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436
- Aaron Aaron |
Lisa |
- 
- Olivia 
+ Gourab |
||||
|---|---|---|---|---|---|---|---|
| Alumni | +Alumni | |||||||
|---|---|---|---|---|---|---|---|---|
| @@ -395,7 +975,11 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436 |
- Shivang Shivang |
+
+
+ Olivia |
||||||
| + |
Boris Glavic (IIT) |
- + |
Su Feng (IIT) |
@@ -451,27 +1035,10 @@ Sampling (x10), 300, 242.5666234549135, 300, 119.61607021316885, 162.00108394436 |
Mimir is supported by NSF Award ACI-1640864, NPS Award N00244-16-1-0022, and gifts from Oracle
+Mimir is supported by NSF Award ACI-1640864, NPS Award N00244-16-1-0022, and gifts from Oracle
-
-
- It's not the data that's uncertain, it's the interpretation. -
- Tagged best-guess evaluation is faster and easier to understand. -
- Not committing to one representation allows faster query processing. -
Thanks!
- -