text stringlengths 30 4k | source stringlengths 60 201 |
|---|---|
1. Any birational map φ : S ��� S� is dominated by a nonsingular
S, S� which are compositions of
surface S with birational morphisms q, q� : S
blow-up maps, i.e.
→
(4)
S
q
� �
S
��������
q�
� �
� S�
φ
Proof. First resolve the indeterminacy of φ using S and then note that q� is a
�
birational morphism, i.e. a... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
g − 2 = E (E + K).
·
·
Theorem 3 (Castelnuovo). Let S be a projective surface and E ⊂ S a curve
∼ P1 with E2 =
s.t. it is a blowup and E is
=
the exceptional curve (classically called an “exceptional curve of the first kind”).
Then ∃ a morphism S →
−1.
S�
Proof. We will find S� as the image of a particular morphism ... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
.
Now, consider the exact sequence
(5)
O → OS (H + (i − 1)E) → OS (H + iE) → OE (k − i) ∼
= OS (H + iE)
|E →
0
for 1 ≤ i ≤ k + 1. We know that H 1(E, OE (k − i)) = 0, so we get
(6)
0 →H 0(S, OS (H + (i − 1)E)) → H 0(S, OS (H + iE)) → H 0(E, OE (k − i)) →
H 1(S, OS (H + (i − 1)E)) → H 1(S, OS (H + iE)) → 0
Thus, t... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
is enough to show that M |E is generated by
global sections on E. Now, M E = OE (k − k) = OE is generated by the global
section 1. Therefore, lifting it to a section of H 0(S, M ) and using Nakayama’s
lemma, we see that M is generated by global sections at every point of E as well.
f � Pn for some N . Let S� be the... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
→
→
⇒
(7)
Rif∗(F)∧
y
n
∼ lim H i(Xn, Fn)
→ ←−
where Xn = X ×y Spec OY /my is the thickened scheme-theoretic preimage of
y. We’ll apply it with i = 0, F = OS, f : S
S0. f∗OS = OS0 since S0 is
ˆ
Op ←−
normal. Moreover,
is
2-dimensional ∼
→
= lim H 0(En, OEn ). Now, it is enough to show that
ˆ
Op
= k[[x, y]... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
2 = k ⊕ kx ⊕ ky.
Now inducting, we find that H 0(OEn ) is isomorphic to k[x, y]/(x, y)n . Lift
elements x, y to H 0(OEn+1 ), we find that H 0(OP1 (n) is a vector space with
basis xn, xn−1y, . . . , yn (contained in the symmetric power of (x, y)). So we
∼
get H 0(OEn+1 ) ∼ k[x, y]/(x, y)n+1 . The truncations are compa... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
Kinematics of Rigid Bodies
1
2.003J/1.053J Dynamics and Control I, Spring 2007
Professor Thomas Peacock
2/28/2007
Lecture 7
2-D Motion of Rigid Bodies - Kinematics
Kinematics of Rigid Bodies
Williams 3-3 (No method of instant centers)
”Kinematics” - Description and analysis of the motions of objects without con
s... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
ating. Figure by MIT OCW.
Therefore:
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and
Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Kinematics of Rigid Bodies
3
dR
dt
... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
Diagram of Rod CD. Figure by MIT OCW.
Angular velocity is ωCD = dθ eˆz
dt
ωCD is independent of choice of point C. Bar has intrinsic rotation.
The motion of a rigid body is expressed as a combination of translation of a
point fixed on the body and rotation about an axis passing through this point
→ need (x, y, θ).
... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
Compute the velocity of any point P on a rigid body.
Now:
ω =
Rp = RG + r
dθ
eˆzdt
dRG
dt
p
d
v = R =
p
dt
vp = vG + ω × r
Use vp = vG + ω × r. This relationship will be used often in finding the velocity
of the body needed for the angular momentum principle.
dr
dt
+
vP = vG + ω × r
We can express the mo... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
of the bar is ωAB = θ˙eˆz.
vB = vA + ω × rAB
vA = x˙ eˆx
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and
Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Kinematics of Rigi... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
complete set of coordinates may not be independent; however, due to geo
metric constraints.
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and
Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
07. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
Kinematics of Rigid Bodies
10
Figure 13: Hoop rolls along x-direction where distanced travelled equals rθ.
Figure by MIT OCW.
This statement means the displacement xc is equal to the part of the hoo... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1f67510b4e0e8758705be60bc6957982_lec07.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
6.006 Introduction to Algorithms
Spring 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Lecture 4
Balanced Binary Search Trees
6.006 Spring 2008
Lecture 4: Balanced Binary Search Trees
Lecture Overview
• The importance ... | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2008/1f940ab45156183a323edd0011317452_lec4.pdf |
Path Lecture 4
Balanced Binary Search Trees
6.006 Spring 2008
AVL Trees:
Definition
AVL trees are self-balancing binary search trees. These trees are named after their two
inventors G.M. Adel’son-Vel’skii and E.M. Landis 1
An AVL tree is one that requires heights of left and right children of every node to differ
... | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2008/1f940ab45156183a323edd0011317452_lec4.pdf |
2Nh−2
⇒ Nh > 2h/2
= h <
⇒
1
2
lg h
Alternatively:
Nh > Fn
In fact,Nh = Fn+2 − 1
(nth Fibonacci number)
(simple induction)
φh
Fh = √
5
1 +
2
√
5
where φ =
(rounded to nearest integer)
≈ 1.618
(golden ratio)
= ⇒ maxh ≈
logφ(n) ≈ 1.440 lg(n)
AVL Insert:
1. insert as in simple BST
2. work your way up ... | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2008/1f940ab45156183a323edd0011317452_lec4.pdf |
1. In general, process may need several rotations before an Insert is completed.
Comment 2. Delete(-min) harder but possible.
6
654120115029263211φφφ6541201150292621φφφ123Insert(23)x = 29: left-left case654120115026233211φφφ65412011501φφDoneInsert(55)29φ322623129φφ65412011502φφ22623129φφx=65: left-right case551554120... | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2008/1f940ab45156183a323edd0011317452_lec4.pdf |
several
operations =
fast on average.
⇒
7
Lecture 4
Balanced Binary Search Trees
6.006 Spring 2008
Splay Trees
Upon access (search or insert), move node to root by sequence of rotations and/or double-
rotations (just like AVL trees). Height can be linear but still O(lg n) per operation “on
average” (amortized)
... | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2008/1f940ab45156183a323edd0011317452_lec4.pdf |
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.438 Algorithms for Inference
Fall 2014
8
Inferences on trees: sum-product algorithm
Recall the two fundamental inference problems in graphical models:
1. marginalization, i.e. computing the marginal distribution p... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
can be applied to obtain the MAP estimate.
N operations.
X
|
|
8.1 Elimination algorithm on trees
Recall that a graph G is a tree if any two nodes are connected by exactly one path.
1 edges and no cycles.
This definition implies that all tree graphs have exactly N
Throughout this lecture, we will use the recurrin... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
Figure 3: A star-shaped graph and the resulting graph after eliminating variable x1.
2
x1x2x3x4x5x1x3x4x5x1x3x5x1x3x1x1x6x2x3x4x5x6x2x3x4x5 Figure 4: The sequence of graph structures and messages obtained from the elimina
tion algorithm on the graph from Figure 1 using an optimal ordering (4, 5, 3, 2, 1).
Fortunat... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
we will assume a redundant representation with unary potentials φi(xi) for each
variable xi. In other words, we assume the factorization
px(x) =
1
Z
φi(xi)
ψij (xi, xj ).
i∈V
(i,j)∈E
(1)
The messages produced in the course of the algorithm are:
m4(x2) =
φ4(x4)ψ24(x2, x4)
m5(x2) =
m3(x1) =
m2(x1) =
x4
x5
x3
x2 ... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
|
1 edges in the graph, the total
2), i.e. linear in the graph size and quadratic in the alphabet
|
X
−
X
|
|
|
8.2 Sum-product algorithm on trees
Returning to Figure 1, suppose we want to compute the marginal for another variable
x3. If we use the elimination ordering (5, 4, 2, 1, 3), the resulting messages are: ... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
messages such that the prerequisites are available at
each step. One way to do this is through the following two-step procedure.
, as shown in Figure 6. (Note: the
N (i)
\ {
∈
}
\
j
1Note that this analysis does not include the time for computing the products in each of the
messages. A naive implementation would,... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
This view will become clearer when we
discuss hidden Markov models.
8.3 Parallel sum-product
The sum-product algorithm as described in Section 8.2 is inherently sequential: the
messages must be computed in sequence to ensure that the prerequisites are avail
able at each step. However, the algorithm was described i... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
) can be viewed as a fixed point update
for (6). You will prove in a homework exercise that this procedure will converge to
the correct messages (6) in d iterations, where d is the diameter of the tree (i.e. the
length of the longest path).
Note that this parallel procedure entails significant overhead: each iteratio... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
of neighbors) of node i.
N computations. This must be done for each of the N
a
−
X
X
X
i
|
|
|
|
|
However, in parallel sum-product, we can share computation between the different
messages by computing them simultaneously as follows:
1. Compute
⎛
i(xi) = ⎝
µ t
(cid:89)
⎞
k→i(xi)⎠ φi(xi)
m t
k∈N (i)
2. For all... | https://ocw.mit.edu/courses/6-438-algorithms-for-inference-fall-2014/1faaccb44f78c4f4e99c6814842082a0_MIT6_438F14_Lec8.pdf |
Corn Sheller
This project is a low-cost device for removing corn kernels from the cob. It is made from a piece
of sheet metal which is formed and then joined together. This device was developed by Marco
Villagarcia, an engineer from Cusco, Peru, based on an injection molded plastic corn sheller from
Malawi. It is ma... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/1fab1f92881a2a0aa9ee50b0154a1960_MITEC_720JS10_bldit_csm.pdf |
an
arbor press or vice can be used to generate sufficient force to bend the
metal. Mark the position of the ridges on your part and then use the die to
bend the ridges.
Forming the Cone
You can form the cone by bending it over an anvil or a piece of pipe, by
hand or with a hammer or you can bend the whole things by... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/1fab1f92881a2a0aa9ee50b0154a1960_MITEC_720JS10_bldit_csm.pdf |
two pieces are joined through a melting
and re-solidification process. Spot-welding allows rapid welding of
thin materials that do not require a complete weld seam. Two copper
electrodes hold the sheets together and then deliver enough current
through the sheets in a concentrated area that the sheets melt together ... | https://ocw.mit.edu/courses/ec-720j-d-lab-ii-design-spring-2010/1fab1f92881a2a0aa9ee50b0154a1960_MITEC_720JS10_bldit_csm.pdf |
Introduction to Engineering
Introduction to Engineering
Systems, ESD.00
Networks III/Stakeholders
Lecture 9
Lecturers:
Professor Joseph Sussman
Dr. Afreen Siddiqi
TA: Regina Clewlow
f
Outline
Outline
Introduction to networks (Lecture 8)
Infrastructure networks ((Lecture 8))
Institutional networks (Lecture 8)... | https://ocw.mit.edu/courses/esd-00-introduction-to-engineering-systems-spring-2011/1fc7ee99f40b5f81cfa1765ed1304033_MITESD_00S11_lec09.pdf |
z What are its characteristics?
References
References
[1]M.E.J. Newman, “The structure and function of complex networks”, SIAM
[1]M E J Newman The structure and function of complex networks SIAM
review, 2003
[2] Duncan J. Watts & Steven H. Strogatz, “Collective dynamics of ‘small
[2] Duncan J. Watts & Steven H. Str... | https://ocw.mit.edu/courses/esd-00-introduction-to-engineering-systems-spring-2011/1fc7ee99f40b5f81cfa1765ed1304033_MITESD_00S11_lec09.pdf |
Power
• Legitimacy
• Urgency
Urgency
St eholder
s
Stakeholders
ak
S k
Stakehholdld er
ill be positively
salience
1:
PProposiitiion 1
related
the cumulative number of stakeholder
attributes –power, legitimacy, and urgency –perceived by
(Mitchell)
present. (Mitchell)
managers toto bebe present
managers
w... | https://ocw.mit.edu/courses/esd-00-introduction-to-engineering-systems-spring-2011/1fc7ee99f40b5f81cfa1765ed1304033_MITESD_00S11_lec09.pdf |
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
Physics 8.07: Electromagnetism II
Prof. Alan Guth
September 21, 2012
LECTURE NOTES 4
CONDUCTORS: SURFACE FORCES AND CAPACITANCE
These notes are an addendum to Lecture 7, Wednesday September 19, 2012. The
notes will not repeat what I said in class, but rather will... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
��
4π(cid:8)0r2
(cid:6)0
have
(cid:6)E · d(cid:6)(cid:13)
∞
(cid:4)
= +
r
∞
(cid:6)E · d(cid:6)(cid:13) =
Q
4π(cid:8)0
(cid:4) ∞ dr
r2
r
=
Q
4π(cid:8)0r
.
(4.2)
(4.3)
8.07 LECTURE NOTES 4, FALL 2012
p. 2
The potential on the surface is therefore Q/(4π(cid:8)0R, and the potential inside the sphere
is constant, with thi... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
is
(4.6)
dWmech = d (cid:6)F · (ˆr dR) = P da dR .
Integrating over the surface, the total mechanical work done is
(cid:4)
dWmech = P dR
da = 4πR2P dR .
(4.7)
(4.8)
Even though we have integrated, I am still calling the work dWmech, since it is an in-
finitesimal quantity proportional to dR. From Eq. (4.5), the change i... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
real charge layer will have some nonzero thickness.
If we model the charge density as being uniform over this thickness, the situation is
described in the following diagram:
Gauss’s law implies that the electric field at any point is proportional to the enclosed
charge, so the electric field varies linearly with distance... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
)
(cid:6)E = 0
outside the conductors, and on the boundaries of each conductor
(cid:6)
E = n ,ˆ
⊥
σ
(cid:8)0
(cid:6)
E = 0 ,
(cid:3)
⊥
where (cid:6)E is the normal contribution of the electric field, (cid:6)E is the tangential contribution,
and nˆ is a unit outward normal vector to the surface. The total charges on each... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
the geometry of the conductors. This matrix
can be inverted, so we can write
Qi =
(cid:5)
j
Cij Vj ,
(4.16)
where as a matrix,
C = P −1 , or equivalently
(cid:5)
j
CijPjk = δik .
(4.17)
Cij is called the capacitance matrix, while Pij is called either the elastance matrix, or
simply the reciprocal capacitance matrix. In... | https://ocw.mit.edu/courses/8-07-electromagnetism-ii-fall-2012/1ffda29d6ddadef8e37e4be9c071b4e7_MIT8_07F12_ln4.pdf |
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MIT OpenCourseWare
https://ocw.mit.edu
2.062J / 1.138J / 18.376J Wave Propagation
Spring 2017
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/2-062j-wave-propagation-spring-2017/201818c21f2a69ccbd7afc473b5aa143_MIT2_062J_S17_Chap5.pdf |
Machine Learning for Healthcare
HST.956, 6.S897
Lecture 1: What makes healthcare unique?
Prof. David Sontag & Pete Szolovits
1
The Problem
• Cost of health care expenditures in the US are
over $3 trillion, and rising
• Despite having some of the best clinicians in
the world, chronic conditi... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
is one of the symptoms
that the patient had 5 days ago
FIGURE 1-1 Major parts of an expert system. Arrows indicate
information flow.
© Addison-Wesley Publishing Company, Inc. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/
FIGURE 33-1 Short ... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
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cP<::-1)-/)6:$()d*'()"5M- -/)6:$()d%2e
5 1980’s: automating medical discovery
Discovers that prednisone
elevates cholesterol
(Annals of Internal Medicine, ‘86)
[Robert ... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
.mit.edu/help/faq-fair-use/
7
Outline for today’s class
1. Brief history of AI and ML in healthcare
2. Why now?
3. Examples of how ML will transform
healthcare
4. What is unique about ML in healthcare?
5. Overview of cla... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
()
;@/-9()n
© Lab for Computational Physiology. All rights reserved. This content is excluded from our Creative Commons license.
For more information, see https://ocw.mit.edu/help/faq-fair-use/
10
Large datasets
President Obama’s initiative to create a 1 million
person research cohort
Core data set:
• Basel... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
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! ,6A@16/@1O)/-9/93),NWXB
.@F-9
! ?56176.O3)X6/<@;6:)L10K
B@F-9)YXLB9Z
! G;<C<-F)P-F<.6:),6;K06K-
"O9/-7)YGP,"Z3)7<::<@;9)@C
7-F<.6:).@;.-E/9
© (cid:45)O(cid:42)(cid:47)C. All rights reserved. This content is excluded
from our Creative Commons... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
content is excluded from our Creative Commons license. For more information,
see https://ocw.mit.edu/help/faq-fair-use/
17
Breakthroughs in machine learning
• Major advances in ML & AI
– Learning with high-dimensional features (e.g., l1-
regularization)
– Semi-supervised and unsupervised learning
– Modern dee... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
5-)E6/<-;/Q9)
.@;F</<@;9)Y.011-;/)6;F)C0/01-Z
C:0 E;-07@;<6 F<6A-/-9
L<9-69-9
"O7E/@79
C6/<K0-
.@0K5
.5-9/
5<K5
E6<;
b2B
E6<; b2B
b0/@76/<.6::O)-D/16./-F)C1@7)
-:-./1@;<.)5-6:/5)1-.@1F
L1<H-9
! ]-//-1)/1<6K-
! l69/-1)F<6K;@9<9
! S61:O)F-/-./<@;)@C
6FH-19-)-H-;/9
! ?1-H-;/)7-F<.6:
-11@19
25 456/)M<::)/... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
456/)M<::)/5-)S^)@C)/5-)C0/01-)A-):<8->
^-F0.<;K)/5-);--F)C@1)9E-.<6:<9/).@;90:/9
Input
Chest X-Ray Image
CheXNet
121-layer CNN
Output
Pneumonia Positive (85%)
b115O/57<6>
© (cid:51)a(cid:75)pur(cid:76)ar et al. All rights reserved. This content is excluded from our
Creative Commons license. For more informat... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
Undiagnosed
condition
#<7-
Courtesy of the CDC. Image is in the public domain.
l<K01-).1-F</3)5//E93``MMM$.F.$K@H`8<F;-OF<9-69-`E1-H-;/<@;_1<98$5/7:
31 456/)<9)/5-)C0/01-)@C)5@M)M-)/1-6/)
.51@;<.)F<9-69->
! ?1-F<./<;K)6)E6/<-;/Q9)C0/01-)F<9-69-)E1@K1-99<@;
! ?1-.<9<@;)7-F<.<;-
S$--9%&+(,%*90(/%&'(0$'*"C<(%&(@Q/0%... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
3. Examples of how ML will transform
healthcare
4. What is unique about ML in healthcare?
5. Overview of class syllabus
34
What makes healthcare different?
• Life or death decisions
– Need robust algorithms
– Checks and balances built into ML deployment
– (Also aris... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
6.S897/HST.956 vs 6.874
• Our class will focus on clinical data and its use
to improve health care
• For reasons of time & scope, we will not go
deep into applications in the life sciences
– For this, we recommend taking 6.874
Computational Systems Biology: Deep Learning
in the Life Sciences
39
... | https://ocw.mit.edu/courses/6-s897-machine-learning-for-healthcare-spring-2019/2020812c6b3be9e2c27873595d1a9aed_MIT6_S897S19_lec1.pdf |
6.852: Distributed Algorithms
Fall, 2009
Class 3
Today’s plan
• Algorithms in general synchronous networks (continued):
Shortest paths spanning tree
Minimum-weight spanning tree
Maximal independent set
• Reading: Sections 4.3-4.5
• Next:
– Distributed consensus
– Reading: Sections 5.1, 6.1-6.3
Last time... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
e.g. latency.
– UIDs.
– Nodes know weights of incident edges.
– Nodes know n (need for termination).
• Required:
– Shortest-paths tree, giving shortest paths from i0 to every other node.
– Shortest path = path with minimum total weight.
– Each node should output parent, “distance” from root (by weight).
Shorte... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
4
1
6
3
8 0
4
0
9
6
3
Round 1 (msgs)
Shortest paths
7
2
10
11 5 1
11
1
6
3
8 0
4
0
9
6
3
5
2
0
2
4
Round 1 (trans)
Shortest paths
2
5
10
1
4
2
4
5
2
11 1
8
6
3
3
7
11
0
9
6
Round 2 (start)
Shortest paths
7
2
10
... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
0
2
4 2
11 1
11
19 8 0
6
3
19
6
3
0
9
6
4
6
6
Round 3 (msgs)
Shortest paths
10
1
3
7
2
3
11 3 5 2 1
310
11
19 8 0
6
3
9
6
3
4
0
9 6
6
6
5
2
0
2
4 2
Round 3 (trans)
Shortest paths
3
2
5
10
1
4
2
4
5
2
10
1
8
6
3
9
3
7
11
0
9
6
6
Round 4 (start)
Shortest paths
10 1
3
7
2
3
11 3 5 2 1
310
1... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
5 2 1
310
10
9 8 0
6
3
9
6
3
4
0
9 6
6
6
5
2
0
2
4 2
Round 5 (msgs)
Shortest paths
10
1
3
7
2
3
11 3 5 2 1
310
10
9 8 0
6
3
9
6
3
4
0
9 6
6
6
5
2
0
2
4 2
Round 5 (trans)
Shortest paths
3
2
5
10
1
4
2
4
5
2
10 1
8
6
3
9
3
7
11
0
9
6
6
End configuration
Correctness
z Need to show... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
really is the distance on some at-
most-r-hop path to i, and parent is its parent on such a path.
z LTTR---easy use of inductive hypothesis.
z But we must still argue that disti and parenti correspond to a shortest
at-most-r-hop path.
Correctness
z Key invariant: After r rounds:
Every process i has its dist and... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
Q: Does the time bound really depend on n, or is it O(diam)?
z A: It’s really n, since “shortest path” can be over a path with more links.
z Example:
79
i0
1
1
1
i0
i0
i0
1
i0
1
i
Bellman-Ford Shortest-Paths
Algorithm
• Will revisit Bellman-Ford shortly in asynchronous
networks.
• Gets even more expens... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
forest of G. Fix any
j, 1 d j d k . Let e be a minimum weight outgoing edge of Tj.
Then there is a spanning tree for G that includes all the Tis and e,
and has minimum weight among all spanning trees for G that
include all the Tis.
• Proof:
– Suppose not---there’s some spanning tree T for G that includes all the T... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
ifies the following concurrent strategy:
z At each stage, suppose (inductively) that the current forest contains only
edges from the unique MST.
z Now several components choose MWOEs concurrently.
z Each of these edges is in the unique MST, by Lemma 1.
z So OK to add them all (no cycles, since all are in the same ... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
all components to find MWOEs.
– Leader of each level k component tells endpoint nodes of its
MWOE to add the edge for level k+1.
– Each new component has t 2k+1 nodes, as claimed.
Level k o Level k+1, cont’d
• Each level-k component leader finds MWOE of its component.
• Combine level-k components using MWOEs, to o... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spanning tree
4
g
a
d
12
5
c
1
2
f
9
i
10
0
b
8
3
7
e
11
j
6
h
k
13
Minimum spannin... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
n rounds for each level
log n levels, because there are t 2k nodes in each level k component.
Messages: O( (n + |E|) log n)
Naïve analysis.
At each level, O(n) messages sent on tree edges, O(|E|) messages
overall for all the test messages and their responses.
Messages: O(n log n + |E|)
A surprising, s... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
can become the leader) or cross on an edge (choose
endpoint with the larger UID).
– Complexity: Time O(n); Messages O(n)
• Given any weighted connected undirected graph, with known
n, but no leader, elect a leader:
– First use GHS MST to get a spanning tree, then use the
spanning tree to elect a leader.
– Complexit... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
Large enough set so it’s very likely that all numbers are distinct.
• Neighbors exchange vals.
• If node i’s val > all neighbors’ vals, then process i declares
itself a winner and notifies its neighbors.
• Any neighbor of a winner declares itself a loser, notifies its
neighbors.
• Processes reconstruct the remainin... | https://ocw.mit.edu/courses/6-852j-distributed-algorithms-fall-2009/203e61d32dfad9ba4279f269f1e4595b_MIT6_852JF09_lec03.pdf |
Filter Banks: time domain
Filter Banks: time domain
((HaarHaar example) and frequency domain;
example) and frequency domain;
conditions for alias cancellation
conditions for alias cancellation
and no distortion
and no distortion
trivial) example of a two channel FIR
Simplest (non--trivial) example of a two channe... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
i.e.
^^
x[2nx[2n--1] =
1] =
11
� 22
(y00[n][n] –– yy11[n]) = x[2n
(y
[n]) = x[2n--1]1]
^^
x[2n] =
x[2n] =
11
� 22
(y00[n] + y
(y
[n]) = x[2n]
[n] + y11[n]) = x[2n]
fromfrom jj andand kk
^^
So x[n]
So x[n]
=
=
x[n]
x[n]
�
Perfect reconstruction!
Perfect reconstruction!
In general, we will make all f... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
[1][1]
MM
^^ x
x
=
=
LTT BBTT
L
yy00
yy11
----------------mm
----------------
88
�
Perfect reconstruction means that the synthesis
Perfect reconstruction means that the synthesis
bank is the inverse of the analysis bank.
bank is the inverse of the analysis bank.
^^
�
x = x �
x = x
LL
LLTT BBT
T
= I= ... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
FF11(z)(z)
¯
vv11[n][n]
zz--transform definition:
transform definition:
¥
� x[n]z
X(z) = �
X(z) =
¥
n=n=--¥
w
Put z = eeii w
Put z =
x[n]z--nn
to get DTFT
to get DTFT
x[n]x[n]^^
1010
fl
fl
›
›
¯
¥
Perfect reconstruction requirement:
Perfect reconstruction requirement:
time delays)
(ll time delays)
(
^^
]
x... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
}
In frequency domain:
In frequency domain:
or X(eeiiw
or X(
w ))
fi X(X(w
X(z)X(z)
)
)
w ++ p
fi X(X(w
X(X(--z)z)
w
fi
X(zX(z½½)) fi
)
X(
X(
)
w
(
) =) = ½½{H{H00(
22
) X(
) X(
22
p ))
YY00((w
w
w
( + p
) + H00( +
) + H
22
22
w
p )X(
)X( ++ p
22
p )})}
1212
fi
w
fi
w
w
w
w
w
w
Suppose X(w
Suppos... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
1(z) H(z) H11(z) = 2z
(z) = 2z-- ll
--------------jj
--------------
2)2) Condition for alias cancellation (no term in X(
Condition for alias cancellation (no term in X(--z))z))
FF00(z) H(z) H00((--z) + F
z) = 0
z) + F11(z) H(z) H11((--z) = 0
--------------kk
--------------
To satisfy alias cancellation condition, ... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
So we can rewrite Equation
zz-- ll P(z) + z
P(z) + z-- ll P(P(--z) = 2z
z) = 2z-- ll
i.e.
i.e.
z) = 2
P(z) + P(--z) = 2
P(z) + P(
---------------------------pp
---------------------------
This is the condition on the normalized product filter
This is the condition on the normalized product filter
for Perfect Reco... | https://ocw.mit.edu/courses/18-327-wavelets-filter-banks-and-applications-spring-2003/204a826459bc8236e14f4787e1575cc2_Slides3.pdf |
6.867 Machine learning, lecture 9 (Jaakkola)
1
Lecture topics:
• Kernel optimization
• Model (kernel) selection
Kernel optimization
Whether we are interested in (linear) classification or regression we are faced with the
problem of selecting an appropriate kernel function. A step in this direction might be to
ta... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
in the kernel
representation as follows
K˜ (x, x�) = �
K(x, x�)
K(x, x)K(x�, x�)
(1)
Another approach to optimizing the kernel function is kernel alignment. In other words,
we would adjust the kernel parameters so as to make it, or its Gram matrix, more towards
an ideal target kernel. For example, in a classifica... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
as to make the Gram matrix of this kernel, Kij (θ), more similar to the Gram matrix of
∗ . To do this we view the Gram matrices as vectors and define their
the target kernel, Kij
inner product in the usual way
i=1
i=1
�K ∗, Kθ� =
n
�
i,j=1
Kij
∗ Kij (θ)
(5)
The parameters θ can be now set so as to maximize t... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
T x�) or
K2(x, x�) = (1 + x T x�)2
(7)
(8)
1In statistics, a model is a family/set of distributions or a family/set of linear separators.
Cite as: Tommi Jaakkola, course materials for 6.867 Machine Learning, Fall 2006. MIT OpenCourseWare
(http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
⊆ F2. For purposes of classification, we wouldn’t actually have to assert
that the families of discriminant functions are nested, only that the discriminant functions
in F2 can produce the signs of those in F1.
The formal problem for us to solve is then to select a kernel Ki from a set of possible kernels
K1, K2, . ... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
we chose
model Fi then we would find the best fitting discriminant function fˆ i ∈ Fi by minimizing
n
�
�
�
J(θ, θ0) =
Loss yt, f (xt; θ, θ0) + λn�θ�2
(11)
t=1
Cite as: Tommi Jaakkola, course materials for 6.867 Machine Learning, Fall 2006. MIT OpenCourseWare
(http://ocw.mit.edu/), Massachusetts Institute of Tec... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
example, our goal may be to
minimize classification error so that Loss∗(y, f (x)) = 1 − δ(y, sign(f (x))), i.e., the zero-one
loss. We could still estimate the SVM classifier from the training set in the usual way,
optimizing the hinge loss. The hinge loss can be viewed as a convex surrogate for the
zero-one loss and... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
distributions are the same.
Now, we clearly do not have access to the underlying distribution and therefore cannot
evaluate R(fˆ i). In fact, the whole model selection problem would go away if had access to
the underlying distribution P (x, y). To classify new instances, we would simply forget about
the training se... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
the labels and examples were linear (the
minimum probability of error classifier is linear), then the quadratic nature of the resulting
decision boundary would simply be due to noise and couldn’t generalize very well. So we
should be able to see an increasing gap between the training and test errors as a function
of... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
6.867 Machine learning, lecture 9 (Jaakkola)
that we would like to have and the empirical risk Rn(fˆ i)
Rn(fˆ i) =
1
n
n
�
�
�
Loss∗ yt, fˆ i(xt)
t=1
6
(15)
that we can compute. If we can do this, then we have a partial access to R(fˆ i) through its
empirical counterpart Rn(fˆ i). Note that the empirical r... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
increasing function of i,
the model order (e.g., the degree of polynomial kernel). Moreover, the penalty should go
down as a function n. In other words, the more data we have, the more complex models
we expect to be able to fit and still have the training error close to the generalization error.
The type of result i... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/2051efc0159bf145f2050469b7589fc5_lec9.pdf |
6.863J Natural Language Processing
Lecture 16: the boundaries of syntax &
semantics – towards constraint-based
systems
Robert C. Berwick
The Menu Bar
• Administrivia:
• Lab 4 due April 9? (what about Friday)
• Start w/ final projects, unless there are
objections
• Agenda:
• Shallow instead of ‘deep’ semantic... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
16 Sp03
Another Example
Syntax:
S � NP VP
VP � V NP
NP �
Det N
Semantics:
S : Apply(VP, NP)
VP : Apply(V, NP)
NP : Apply(lambda (x) (DEF/SING x), N)
Lexicon:
V:kissed = lambda(o) lambda(x) (kiss past
[agent x] [theme o])
N:guy = person
N:dog = DOG
Det:the = DEF/SING
:
Top-down parse sentence
The guy ki... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
(x) (kiss past [agent x] [theme DEF/SING DOG]), (DEF /SING Person))
(kiss past [agent DEF/SING Person] [theme DEF/SING DOG])
6.863J/9.611J Lecture 16 Sp03
Semantic Grammar: Definition
• Syntactic and semantic processing is collapsed
in a single framework
• Like a regular grammar but terminal symbols
are replaced... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
OD � for PERSON
FLIGHT-NP � ART FLIGHT-NOUN
FLIGHT-NP � ART FLIGHT-NOUN
FLIGHT-MODS
FLIGHT-MODS � FLIGHT-MOD
FLIGHT-MODS
FLIGHT-MODS � FLIGHT-MOD
FLIGHT-MOD � from SOURCE
LOCATION
FLIGHT-MOD � to DEST -LOCATION
Parse this sentence (bottom-up):
Book a flight from Boston to Chicago for me
6.863J/9.611J Lectur... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
Boston] [FLIGHT-MODS [FLIGHT
MOD to DEST-LOCATION Chicago]]]]] for me
• RES-MOD � for PERSON
[RESERVING RESERVE-VERB Book [FLIGHT-NP ART a FLIGHT-NOUN flight [FLIGHT
MODS [FLIGHT-MOD from SOURCE-LOCATION Boston] [FLIGHT-MODS [FLIGHT
MOD to DEST-LOCATION Chicago]]]]] [RES-MOD for PERSON me]
• RES-VP � RESERVING RE... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
accused the Farabundo Marti National Liberation Front (FMLN) of the
crime. (...)
Garcia Alvarado, 56, was killed when a bomb placed by urban guerrillas on
his vehicle exploded as it came to a halt at an intersection in downtown San
Salvador.
Vice President -elect Francisco Merino said that when the attorney-genera... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
• Precision
= # correct answers
# total answers
• Recall = # correct answers
# possible correct answers
• Fß =
((ß² + 1) x P x R)
(ß² x P x R)
6.863J/9.611J Lecture 16 Sp03
Architecture – Steps 1 to 3
• Tokenization � split words and punctuation
• He is mr. Jones! � He is mr. Jones !
• Named-entity recognit... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
<joint-venture> with
<companies>
• <produce> <product>
• <company> <capitalized> at <currency>
• <company> <start> <activity> in/on <date>
• Fusion of event structures referring to the
same event = (co-)reference resolution
6.863J/9.611J Lecture 16 Sp03
FASTUS – Evaluation
• MUC-4:
• 44% recall and 55% precis... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
categorization?
• Example:
• consider: __ NP[acc] {AdjP, NP, VP[inf]}
• regard: __ NP[acc] as {NP, AdjP}
• think: __ CP[that], __ NP[acc] NP
There are standard examples for these – cf.
Lab 3.
6.863J/9.611J Lecture 16 Sp03
Example – consider w/ no ‘as’
• John considers vanilla to be an
acceptable flavor
• John ... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
said he
considers them as having championship potential.
• Culturally, the Croats consider themselves as
belonging to the “civilized” West, …
6.863J/9.611J Lecture 16 Sp03
Regarding the NY Times
• As 70 to 80 percent of the cost of blood tests, like
prescriptions, is paid for by the state, neither physicians
nor... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
863J/9.611J Lecture 16 Sp03
Incorporating knowledge
• Do density estimation
P(form | meaning context)
6.863J/9.611J Lecture 16 Sp03
Application: retire
• Step 1: look at what dictionary or wordnet has
for subcat
• Result: intrans; transitive NP; PP (to, from)
• Step 2: see whether these examples attested
(viz... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
of getting PP[from])
6.863J/9.611J Lecture 16 Sp03
We can recalculate entire frame
0.25
=
• P(NP[subj]___|V=retire)
• P(NP[subj]___NP[obj]|V=retire) =
0.50
• P(NP[subj]___PP[from]|V=retire) = 0.04
• P(NP[subj]___PP[from]PP[after]|V=retire) =
0.003
…
(Sum of pr’s of all frames
adds to 1)
6.863J/9.611J Lectu... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
J Lecture 16 Sp03
So…
• Payoff: this knowledge builds parsers that
do very, very well – the best
• How can we acquire this info
automatically?
6.863J/9.611J Lecture 16 Sp03
Lerner (Brent 1993)
• Cues
• A pattern that can be matched against unrestricted
text
• NP NP � (OBJ|SUBJ_OBJ|CAP) (PUNC|CC)
• […] greet... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
16 Sp03
-
-
�
�
‡
Hypothesis Testing – Example
(
i
v P
(
=
p
E
)
=
(
i
v C
0
j
c
,
)
‡
j
f
n
)
�
=
m
=
mr
(
r
e 1
j
)
n
r
e
j
�
�
Ł
�
n
�
r
ł
• Verb = greet � occurs 80 times (n = 80)
• Cue = (OBJ|SUBJ_OBJ|CAP) (PUNC|CC) � has
e = 0.25
• Frame = NP__ NP
• C(greet,(OBJ|SUBJ_OBJ|CAP... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
Reject � PE = 0.011 < 0.02
6.863J/9.611J Lecture 16 Sp03
-
-
�
�
-
-
-
-
�
�
-
-
�
�
Ł
ł
�
�
�
�
Ł
ł
�
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�
�
Ł
ł
Evaluating Lerner
• Very high precision � always close to
100%
• Recall is lower � only 60%
• Only for six frames …
6.863J/9.611J Lecture 16 Sp03
We can start adding pr’... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/20c08c6b52614f6bc8ebbb0d7d7a457e_lecture16bw_03.pdf |
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