DecisionGuidance Management Systems DGMS: Toward Unified Data Acquisition, Learning, Prediction and

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Decision-Guidance Management Systems (DGMS)
Toward Unified Data Acquisition, Learning,
Prediction and Optimization

• Alex Brodsky
• Dept. of Computer Science, George Mason
  University
• Joint work with
• X, Sean Wang
• Dept. of Computer Science, University of Vermont

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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Motivation and Challenges by Example

• Dairy Delicious, Inc. produces and sells
• 2 products pA and pB using
• 3 ingredients i1, i2 and i3
• Dairy Delicious, Inc. maintains a historical DB,
  and maintains DB views, including
• Sales (week, marketID, marketIndex,
• priceA, priceB, qtyA, qtyB, revA,revB)
• Production( week, marketID, qtyA, qtyB,
  manufCost,
• qty1, cost1, qty2, cost2, qty3, cost3,
  ingredIndex)

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To support managements decisions, develop a
decision-guidance solution to answer queries such
as

• Q1 Given specific prices for ABCs products,
  what will the expected cost, revenue and profit
  be, both in total and in each market?
• Q2 Given specific prices for ABCs products, in
  each market, what are (i) the probability of
  financial loss and (ii) the probability that the
  demand will be below 2000 units of product pA?
• Q3 Given specific prices for ABCs products,
  find all the markets in which the expected
  revenue exceeds 2M and the probability of cost
  exceeding 1.5M is bounded by 5.
• Q4 What should the prices for ABCs products be
  in each market (except for New York City market),
  so as to maximize the expected total profit, yet
  ensure that the probability of cost exceeding
  1.5M is bounded by 5 in each market?

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DGMS High Level View
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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Stochastic Relational Model

• Stochastic schema S ?1T1, , ?nTn,where
• ?i (i1, , n) - an attribute
• Ti (i1, , n) - a domain type
• SReg ?1, , ?k
• Sprob ?_(k1),, ?n
• S-instance of S a finite set of s-tuples over S
• S-tuple t over S is composed of
• tReg is a k-ary tuple over the attributes SReg
• tProb is an (n-k)-dimension probability density
  function (pdf) over the domain Dom(?k1)????
  ?Dom(?n)

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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Dependency Graph
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Stochastic Transformers

• (Tr1) DEFINE TRANSFORM DemandA(real priceA,
  marketIndex) (real-pdf demandAqty)
• if priceA lt 0.79 expectedDemAqty
  230000else if priceA lt 0.99 expectedDemAqty
  150000else if priceA lt 1.29
  expectedDemAqty 95000else if price lt
  2.99 expectedDemAqty 5000else
  expectedDemAqty 0demandAqty
  expectedDemAqty Gaussian(0,150002)
• (Tr2) DEFINE TRANSFORM manuf(real manufAqty,
  manufBqty) (real i1Qty, i2Qty,
  i3Qty, manufCost)
• i1Qty 0.22 manufAqty 1.35
  manufBqtyi2Qty 1.05 manufAqty 2.75
  manufBqtyi3Qty 0.45 manufAqty 1.78
  manufBqtyexpectedManufCost 0.1 manufAqty
  0.05 manufBqtymanufCost expectedManufCost
  Gaussian(0, 0.02 expectedManufCost)

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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Stochastic Prediction in DG-SQL

• (PV1) DEFINE VIEW PredictedSales
• SELECT , demandAqty demandA(P.priceA,P.marketI
  ndex).demAqty, demandBqty
  demandB(P.priceA,P.marketIndex).demBqty,
  revenueA revA(demandAqty, M.manufAqty,
  P.priceA).revenueA, revenueB
  revB(demandBqty, M.manufBqty, P.priceB).revenueBF
  ROM PlannedPricing P, PlannedManufacturing
  MWHERE P.marketID M.marketID
• (PV2) DEFINE VIEW PredictedManufacturingProcurem
  ent
• SELECT S.marketID, M.inflationIndex,
  manufCost manuf(M.manufAqty,M.manufBqty).manufCo
  st, supplyCost supply(i1Qty,i2Qty,i3Qty,
  M.inflationIndex).supplyCostFROM PredictedSales
  S, PlannedManufacturing MWHERE S.marketID
  M.marketIDLET i1Qty manuf(M.manufAqty,M.manuf
  Bqty).i1Qty, i2Qty manuf(M.manufAqty,M.man
  ufBqty).i2Qty, i1Qty manuf(M.manufAqty,M.m
  anufBqty).i3Qty

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Predicted Summary

• (PV3) DEFINE VIEW PredictedSummarySELECT
  S.marketID, S.priceA, S.priceB, M.manufAqty,
  M.manufBqty, totalRevenue S.revenueA
  S.revenueB, totalCost M.manufCost
  M.supplyCost, profit totalRevenue
  totalCostFROM PredictedSales S,
  PredictedManufacturingProcurement M //see
  PV1 and PV2WHERE S.marketID M.marketID
• (Q3) SELECT P.marketID, P.priceA, P.priceB,
  P.manufAqty, P.manufBqty,
  expectedRevenue expect(totalRevenue),
  expectedCost expect(totalCost),
  expectedProfit expect(profit)FROM
  PredictedSummary P //see PV3WHERE
  expect(P.revenue) gt 2000000 and
  Prob(P.totalCost gt 1500000) lt 0.05
• (Q5) SELECT MAX expect(P.totalRevenue)FROM
  PredictedSummary P //see PV3WHERE
  Prob(P.profit lt 0) gt 0.05

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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Decision Optimization in DG-SQL

• (Q6) SELECT P.marketID, P.priceA, P.priceB,
  P.manufAqty, P.manufBqty,
  expectedRevenue expect(totalRevenue),
  expectedCost expect(totalCost),
  expectedProfit expect(profit)FROM
  PredictedSummary P //see PV3WHERE
  P.marketIDltgt'NYC
• (PV4) DEFINE VIEW PlannedSalesSELECT
  I.marketID, I.marketIndex, priceA ND-null,
  priceB ND-nullFROM marketIndex IASSERT 0.0 lt
  priceA lt 10.0 and 0.0 lt priceB lt 10.0
• (Q4) MAXIMIZE SUM(expectedProfit)ROW ASSERT
  Prob(P.totalCost gt 1500000) lt 0.05
• SELECT P.marketID, P.priceA, P.priceB,
  P.manufAqty, P.manufBqty,
  expectedRevenue expect(totalRevenue),
  expectedCost expect(totalCost),
  expectedProfit expect(profit)FROM
  PredictedSummary P //See PV3, but replacing
  PV1, PV2 with PV4, PV5, resp.WHERE
  P.marketID ltgt 'NYC'

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Syntax of DG-SQL Optimization Queries

• the optimization syntax of DG-SQL involves the
  following.
• MINIMIZE/MAXIMIZE clause needs two items, namely
  aggr and attr, where aggr is an aggregation
  function (such as sum and avg), and attr is an
  attribute name that appears in the SELECT clause.
  Example MAXIMIZE sum(profit).
• ASSERT clause that appears immediately after the
  WHERE clause is syntactically the same as the
  WHERE clause, and ASSERT that appears after the
  GROUP BY clause is syntactically the same as the
  HAVING clause.

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Semantics of DG-SQL Optimization Queries

• consider the optimization query from which
  MINIMIZE/MAXIMIZE and ASSERT clauses removed.
• An instantiation of values in ND-nulls (one value
  for each introduced ND-null) corresponds to an
  output s-relation, with a particular value
  computed in the MINIMIZE/MAXIMIZE clause.
• We say that an s-relation is feasible if it is
  computed from an instantiation to ND-nulls that
  satisfy the conditions in the ASSERT clause(s).
• We say that an s-relation is optimal, if it is
  feasible, and the value of the expression in the
  MINIMIZE/MAXIMIZE clause is minimal/maximal among
  all feasible s-relations.
• The corresponding instantiation of values into
  ND-nulls (ND-instantiation) is optimal.
• The semantics of optimization query in DG-SQL
• (1) finding an optimal ND-instantiation and
  replacing ND-nulls with the corresponding values,
  and
• (2) finding an optimal s-relation.

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Presentation Outline

• Motivation and Challenges by Example
• Stochastic Relational Model
• Dependency Graph and Transformers
• Stochastic Prediction in DG-SQL
• Decision Optimization in DG-SQL
• Regression Learning in DG-SQL
• Conclusions and Future Work

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Regression Learning in DG-SQL

• (Tr3) DEFINE VIEW Coef AS TUPLE (c1ND-Null,
  c2ND-Null, , c8ND-Null)
• DEFINE TRANSFORM expectedManuf(real manufAqty,
  manufBqty) (real i1Qty, i2Qty, i3Qty, ManufCost)
  
• MINIMIZE SUM( (i1Qty - M.i1qty)2 (i2Qty -
  M.i2qty)2 (i3Qty-
  M.i3qty)2 (Cost - M.manufCost)2 ) )
• FROM ManufacturingProcurement M, Coef
• LET i1Qty Coef.c1 manufAqty Coef.c2
  manufBqty, i2Qty Coef.c3
  manufAqty Coef.c4 manufBqty, i3Qty
  Coef.c5 manufAqty Coef.c6 manufBqty,
  
• Cost Coef.c7 manufAqty Coef.c8
  manufBqty

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Conclusion

• Summary of Contributions
• the concept of DGMS
• stochastic relational model
• Dependency graph and transformers to uniformly
  represent stochastic domain knowledge
• DG-SQL query language that extends SQL with
  regression learning, prediction, and
  deterministic and stochastic decision
  optimization
• Many research questions remain open, e.g.,
• Physical data representation
• Efficient algorithms for prediction and
  optimization (iterative probability evaluation,
  optimizing simulation budget, splitting for small
  probability etc.)
• Formal framework for data acquisition
• Prototype system
• ..
• Questions?

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