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MATLAB代写-PS922

时间：2020-12-13

MSc Behavioural and Economic (or Data) Science

PS922: Issues in Psychological Science

Lecture 7c (Memory Models; MATLAB)

Matlab 3:

Models of Human Memory

Plan:

• Models of LTM and categorisation

• A unitary mathematical model of memory (“SIMPLE”)

• Can we account for data taken as evidence for

separate STM and LTM?

•Part 3 of MATLAB assignment

Assignment Part 3

Implement SIMPLE model of memory and explore its behaviour and

limitations

Calculate a serial position curve for a 10-item list: Assume items take 1 s to present,

and recall occurs 1 s after the last item – i.e., if dist contains the temporal distances

of each item at the time of retrieval: dist=[10:-1:1]

What happens to the curve if you add a retention interval?

E.g.: retint = 20; dist=[10:-1:1]+retint

What happens to the curve if you add a temporal gap around one item?

dist=[12:-1:8 6 4:-1:1]

What happens if you change the list length? What happens if you change the c

parameter? Illustrate the effects of both.

Reading

(if needed or useful; won’t be included in class tests

beyond lecture slides)

Nosofsky, R. M. (1992). Similarity scaling and cognitive

process models. Annual Review of Psychology, 43, 25-53.

Brown, G. D. A., Neath, I., & Chater, N. (2007). A temporal

ratio model of memory. Psychological Review, 114, 539-576.

Models of Categorisation and Memory

Exemplar and other models of categorisation

(models of long-term memory)

The SIMPLE model of memory

(apply same machinery to short-term memory)

Categorisation

Categorisation based on properties of objects

Given the colour and shape of a fruit, is it an apple or a banana?

Given the age and income of a US citizen, how likely is the person

to be Republican or Democrat?

Various possibilities:

Rules (if round and red, -> apple)

Prototypes (how similar to typical apple?)

Exemplar models (to be described)

Representational Assumptions 1

Items can be represented in terms of their values along dimensions

• For example, assume that for a US voter we know both age

and income:

Thus it is assumed that items can be

located in terms of their position within a

multidimensional psychological space.

Here we just assume the structure of the

space. But it can be obtained

independently by MDS (multidimensional

scaling) — constructing a space in which

confusable items have closer locations

(see reading)

(Notion of psychological space is crucial)

Representational Assumptions 2

We can then represent knowledge about the political

affiliation of previously encountered exemplars (voters):

Note that knowledge of political affiliation is represented as a

memory of previously encountered exemplars, not as rules or as

prototypes (i.e., the age and income of a “typical” Republican is not

explicitly represented)

Categorising a New Item

Suppose you know the age and income of a “new” person

but not their political affiliation. Will you place them in the

Democrat or Republican category?

Categorising a New Item

Suppose you know the age and income of a “new” person

but not their political affiliation. Will you place them in the

Democrat or Republican category?

Intuitively:

The new item is similar to Democrats (close in psychological space)

The new item is less similar to Republicans

Psychological Space and MDS

Here we are just assuming the structure of the

“psychological space”

But for more realistic applications people have used

multidimensional scaling (MDS) to construct a space in

which the distances between objects reflects their

psychological similarities (as obtained from, e.g., a

similarity-judgement task)

Similarity and Distance

We want items that are close in psychological space to be more similar

So we first need a measure of the distance (di,j) between any pair of items

(items i and j)

Euclidean

The distance between i and j is just

the Euclidean distance between

them in psychological space: di,j = 5

City Block

The distance between i and j is the sum

of the distance between them on

different dimensions: di,j = 7

Distance in Psychological Space

Here we will just use the city block metric

• City block metric generally works best when stimulus dimensions are

“separable” (can be analysed separately, e.g., the length and angle of a

line)

• Euclidean metric works better when stimulus dimensions are

“integral” (e.g., the brightness and saturation of a colour)

Weighting different dimensions

• It is often useful for a participant to pay more attention to a particular

dimension (e.g. income rather than age)

• This is like stretching out the space along one dimension and shrinking

it along others (although the actual underlying space doesn’t change)

Weighting Different Dimensions

For example:

Suppose we have two dimensions, m and n (e.g., dimension m might be

income, while dimension n is age)

We can then give different weights, wm and wn, to the dimensions

The weights must sum to 1: wm + wn = 1

We then weight the distance between i and j on each dimension so that, if

xi,m is the value of item i on dimension m; xi,n is the value of item i on

dimension n, etc., the distance between i and j becomes

di,j = wm|xi,m - xj,m| + wn |xi,n - xj,n|

(this is using the city block metric still)

Distance and Similarity

Now we have a good way of measuring the distance di,j between the

representations of two exemplars in psychological space

How do we turn this into a measure of the similarity between two locations?

Similarity must reduce as distance increases:

Note:

c is a free parameter that

governs the rate at which

similarity reduces with distance

Similarity and Category Membership

Now we can calculate the similarity of the new item

( ? ) to each previously known exemplar separately

We can calculate:

How similar the new item is to Democrats (summed similarity)

How similar the new item is to Republicans (summed similarity)

The Choice Rule

What is the probability of responding “Republican” (R) to item i ?

(summed similarity to Republican)

divided by

(summed similarity to Republicans plus summed similarity to Democrats)

Empirical Application

Exemplar models have proved very successful at

capturing human categorisation data

Artificial stimuli: angle and size of rectangles

Can predict relations between identification,

categorisation, recognition

Temporal Distinctiveness Models of Memory

Plan:

Describe SIMPLE model of memory

See how to implement it

Straightforward enough to interface with economic

models

Aims of the Model

A model of human memory retrieval: Applied to tasks such as serial

recall, free recall, probed recall

• Currently: Many computational models, but task-specific

• Ideal: Same model for many different memory tasks (cf. Ward,

Tan, Bhatarah)

Explore assumption that STM and LTM phenomena need different

models

• No STM-LTM distinction in model

• Apply to data previously taken as evidence for STM/LTM

distinction

• Some long-standing claims for unitary memory system, but

need models to explore the possibility

Key principles

SIMPLE (Scale-Invariant Memory, Perception,

and Learning)

Memory is temporally organised

Memories organised in terms of their temporal distances

Memory retrieval is like temporal discrimination (old claim)

Same principles of forgetting and retrieval apply over short and long

timescales (seconds to weeks)

No forgetting due to trace decay

All forgetting due to interference

Starting Point: Exemplar Models of LTM

Items are located within a multi-dimensional space

Items close to one another will be more similar

(exponential similarity-distance function)

Similar items: easy to categorise together

Similar items: hard to identify and discriminate

Need to consider closeness/similarity along a

temporal distance dimension as well?

Recency Matters

Distance and Discriminability

Consider two telegraph poles separated by 10 m, with the

nearest being 5 m away: Easily discriminable

| | | | | | | | |

But two telegraph poles separated by 10 m, with the nearest

being 55 m away: Difficult

| | | | | | | | |

Led to ratio-rule / temporal disciminability models of recency

effects in memory (Baddeley; Baddeley & Hitch; Bjork & Whitten;

Crowder; Tan & Ward)

Assumption: The confusability of two items in memory

depends on their relative temporal distances atof recall

The confusability of any two items is a function of the

ratio of their temporal distances: Si,j = (Ti/Tj)c.

For example: two items that occurred 4 and 5 s ago will

be more similar to one another (4/5)c than will two

items that occurred 1 and 2 s ago (1/2)c.

Note: The parameter c marks a difference from earlier

ratio-rule models

Confusability as Temporal Distance Ratios

Implementing similarity/confusability as a temporal

distance ratio effectively instantiates the telegraph

pole analogy:

Assumption: The discriminability of a memory item is

inversely related to that item’s similarity to all other items

In other words, items that are confusable with many others (in

terms of their temporal distances) will be less well recalled.

Assumption:

Serial Position Effects

Performance is best plotted as a function of position of last

rehearsal (e.g. Tan & Ward, 2000):

Unitary ratio model of serial position effects may be possible?

(note: primacy effects in normal population are at least partly

due to rehearsal).

Forgetting over Time

Data from Peterson & Peterson (1959)

Forgetting occurs due to increasing proactive interference from earlier items

No forgetting due to trace decay

Phonological Confusability Effects

After a short time interval, STM is reduced for confusable items

Items can be represented in the model in terms of position along both a

temporal and a “phonological confusability” dimension (should really be multi-

dimensional articulatory space but principle is the same)

(Other dimensions important; not included here)

Overview

Exemplar models provide a good account of human

categorisation behaviour

Addition of a temporal dimension allows exemplar

models to be extended to short-term memory data

Assignment Part 3

Implement SIMPLE and explore its behaviour and limitations

Calculate a serial position curve for a 10-item list: Assume items take 1 s to

present, and recall occurs 1 s after the last item – i.e., if dist contains the temporal

distances of each item at the time of retrieval: dist=[10:-1:1]

What happens to the curve if you add a retention interval?

E.g.: retint = 20; dist=[10:-1:1]+retint

What happens to the curve if you add a temporal gap around one item?

dist=[12:-1:8 6 4:-1:1]

What happens if you change the list length? What happens if you change the c

parameter? Illustrate the effects of both.

1) Create a vector of the temporal distances

2) Log transform the temporal distances

3) Calculate the summed similarity of each item’s temporal

distance to every other item’s temporal distance using:

4) Calculate the resulting discriminability of each item

5) Plot the serial position curve

Implementation Steps / Hints

where di,j is distance between items in log space

and c is a free parameter

clear all; clf

clf

c=5; retint=0;

dist=log([10:-1:1]+retint);

for i=1:length(dist)

eta=exp(-c*abs(dist(i)-dist));

discrim(i)=1/sum(eta);

end

%%Note: this could be vectorized for efficiency

plot(discrim,'-om')

axis([0 length(dist) 0 1])

xlabel('Serial Position','fontsize',14)

ylabel('Discriminability','fontsize',14)

set(gcf, 'color', 'white');

A Basis

PS922: Issues in Psychological Science

Lecture 7c (Memory Models; MATLAB)

Matlab 3:

Models of Human Memory

Plan:

• Models of LTM and categorisation

• A unitary mathematical model of memory (“SIMPLE”)

• Can we account for data taken as evidence for

separate STM and LTM?

•Part 3 of MATLAB assignment

Assignment Part 3

Implement SIMPLE model of memory and explore its behaviour and

limitations

Calculate a serial position curve for a 10-item list: Assume items take 1 s to present,

and recall occurs 1 s after the last item – i.e., if dist contains the temporal distances

of each item at the time of retrieval: dist=[10:-1:1]

What happens to the curve if you add a retention interval?

E.g.: retint = 20; dist=[10:-1:1]+retint

What happens to the curve if you add a temporal gap around one item?

dist=[12:-1:8 6 4:-1:1]

What happens if you change the list length? What happens if you change the c

parameter? Illustrate the effects of both.

Reading

(if needed or useful; won’t be included in class tests

beyond lecture slides)

Nosofsky, R. M. (1992). Similarity scaling and cognitive

process models. Annual Review of Psychology, 43, 25-53.

Brown, G. D. A., Neath, I., & Chater, N. (2007). A temporal

ratio model of memory. Psychological Review, 114, 539-576.

Models of Categorisation and Memory

Exemplar and other models of categorisation

(models of long-term memory)

The SIMPLE model of memory

(apply same machinery to short-term memory)

Categorisation

Categorisation based on properties of objects

Given the colour and shape of a fruit, is it an apple or a banana?

Given the age and income of a US citizen, how likely is the person

to be Republican or Democrat?

Various possibilities:

Rules (if round and red, -> apple)

Prototypes (how similar to typical apple?)

Exemplar models (to be described)

Representational Assumptions 1

Items can be represented in terms of their values along dimensions

• For example, assume that for a US voter we know both age

and income:

Thus it is assumed that items can be

located in terms of their position within a

multidimensional psychological space.

Here we just assume the structure of the

space. But it can be obtained

independently by MDS (multidimensional

scaling) — constructing a space in which

confusable items have closer locations

(see reading)

(Notion of psychological space is crucial)

Representational Assumptions 2

We can then represent knowledge about the political

affiliation of previously encountered exemplars (voters):

Note that knowledge of political affiliation is represented as a

memory of previously encountered exemplars, not as rules or as

prototypes (i.e., the age and income of a “typical” Republican is not

explicitly represented)

Categorising a New Item

Suppose you know the age and income of a “new” person

but not their political affiliation. Will you place them in the

Democrat or Republican category?

Categorising a New Item

Suppose you know the age and income of a “new” person

but not their political affiliation. Will you place them in the

Democrat or Republican category?

Intuitively:

The new item is similar to Democrats (close in psychological space)

The new item is less similar to Republicans

Psychological Space and MDS

Here we are just assuming the structure of the

“psychological space”

But for more realistic applications people have used

multidimensional scaling (MDS) to construct a space in

which the distances between objects reflects their

psychological similarities (as obtained from, e.g., a

similarity-judgement task)

Similarity and Distance

We want items that are close in psychological space to be more similar

So we first need a measure of the distance (di,j) between any pair of items

(items i and j)

Euclidean

The distance between i and j is just

the Euclidean distance between

them in psychological space: di,j = 5

City Block

The distance between i and j is the sum

of the distance between them on

different dimensions: di,j = 7

Distance in Psychological Space

Here we will just use the city block metric

• City block metric generally works best when stimulus dimensions are

“separable” (can be analysed separately, e.g., the length and angle of a

line)

• Euclidean metric works better when stimulus dimensions are

“integral” (e.g., the brightness and saturation of a colour)

Weighting different dimensions

• It is often useful for a participant to pay more attention to a particular

dimension (e.g. income rather than age)

• This is like stretching out the space along one dimension and shrinking

it along others (although the actual underlying space doesn’t change)

Weighting Different Dimensions

For example:

Suppose we have two dimensions, m and n (e.g., dimension m might be

income, while dimension n is age)

We can then give different weights, wm and wn, to the dimensions

The weights must sum to 1: wm + wn = 1

We then weight the distance between i and j on each dimension so that, if

xi,m is the value of item i on dimension m; xi,n is the value of item i on

dimension n, etc., the distance between i and j becomes

di,j = wm|xi,m - xj,m| + wn |xi,n - xj,n|

(this is using the city block metric still)

Distance and Similarity

Now we have a good way of measuring the distance di,j between the

representations of two exemplars in psychological space

How do we turn this into a measure of the similarity between two locations?

Similarity must reduce as distance increases:

Note:

c is a free parameter that

governs the rate at which

similarity reduces with distance

Similarity and Category Membership

Now we can calculate the similarity of the new item

( ? ) to each previously known exemplar separately

We can calculate:

How similar the new item is to Democrats (summed similarity)

How similar the new item is to Republicans (summed similarity)

The Choice Rule

What is the probability of responding “Republican” (R) to item i ?

(summed similarity to Republican)

divided by

(summed similarity to Republicans plus summed similarity to Democrats)

Empirical Application

Exemplar models have proved very successful at

capturing human categorisation data

Artificial stimuli: angle and size of rectangles

Can predict relations between identification,

categorisation, recognition

Temporal Distinctiveness Models of Memory

Plan:

Describe SIMPLE model of memory

See how to implement it

Straightforward enough to interface with economic

models

Aims of the Model

A model of human memory retrieval: Applied to tasks such as serial

recall, free recall, probed recall

• Currently: Many computational models, but task-specific

• Ideal: Same model for many different memory tasks (cf. Ward,

Tan, Bhatarah)

Explore assumption that STM and LTM phenomena need different

models

• No STM-LTM distinction in model

• Apply to data previously taken as evidence for STM/LTM

distinction

• Some long-standing claims for unitary memory system, but

need models to explore the possibility

Key principles

SIMPLE (Scale-Invariant Memory, Perception,

and Learning)

Memory is temporally organised

Memories organised in terms of their temporal distances

Memory retrieval is like temporal discrimination (old claim)

Same principles of forgetting and retrieval apply over short and long

timescales (seconds to weeks)

No forgetting due to trace decay

All forgetting due to interference

Starting Point: Exemplar Models of LTM

Items are located within a multi-dimensional space

Items close to one another will be more similar

(exponential similarity-distance function)

Similar items: easy to categorise together

Similar items: hard to identify and discriminate

Need to consider closeness/similarity along a

temporal distance dimension as well?

Recency Matters

Distance and Discriminability

Consider two telegraph poles separated by 10 m, with the

nearest being 5 m away: Easily discriminable

| | | | | | | | |

But two telegraph poles separated by 10 m, with the nearest

being 55 m away: Difficult

| | | | | | | | |

Led to ratio-rule / temporal disciminability models of recency

effects in memory (Baddeley; Baddeley & Hitch; Bjork & Whitten;

Crowder; Tan & Ward)

Assumption: The confusability of two items in memory

depends on their relative temporal distances atof recall

The confusability of any two items is a function of the

ratio of their temporal distances: Si,j = (Ti/Tj)c.

For example: two items that occurred 4 and 5 s ago will

be more similar to one another (4/5)c than will two

items that occurred 1 and 2 s ago (1/2)c.

Note: The parameter c marks a difference from earlier

ratio-rule models

Confusability as Temporal Distance Ratios

Implementing similarity/confusability as a temporal

distance ratio effectively instantiates the telegraph

pole analogy:

Assumption: The discriminability of a memory item is

inversely related to that item’s similarity to all other items

In other words, items that are confusable with many others (in

terms of their temporal distances) will be less well recalled.

Assumption:

Serial Position Effects

Performance is best plotted as a function of position of last

rehearsal (e.g. Tan & Ward, 2000):

Unitary ratio model of serial position effects may be possible?

(note: primacy effects in normal population are at least partly

due to rehearsal).

Forgetting over Time

Data from Peterson & Peterson (1959)

Forgetting occurs due to increasing proactive interference from earlier items

No forgetting due to trace decay

Phonological Confusability Effects

After a short time interval, STM is reduced for confusable items

Items can be represented in the model in terms of position along both a

temporal and a “phonological confusability” dimension (should really be multi-

dimensional articulatory space but principle is the same)

(Other dimensions important; not included here)

Overview

Exemplar models provide a good account of human

categorisation behaviour

Addition of a temporal dimension allows exemplar

models to be extended to short-term memory data

Assignment Part 3

Implement SIMPLE and explore its behaviour and limitations

Calculate a serial position curve for a 10-item list: Assume items take 1 s to

present, and recall occurs 1 s after the last item – i.e., if dist contains the temporal

distances of each item at the time of retrieval: dist=[10:-1:1]

What happens to the curve if you add a retention interval?

E.g.: retint = 20; dist=[10:-1:1]+retint

What happens to the curve if you add a temporal gap around one item?

dist=[12:-1:8 6 4:-1:1]

What happens if you change the list length? What happens if you change the c

parameter? Illustrate the effects of both.

1) Create a vector of the temporal distances

2) Log transform the temporal distances

3) Calculate the summed similarity of each item’s temporal

distance to every other item’s temporal distance using:

4) Calculate the resulting discriminability of each item

5) Plot the serial position curve

Implementation Steps / Hints

where di,j is distance between items in log space

and c is a free parameter

clear all; clf

clf

c=5; retint=0;

dist=log([10:-1:1]+retint);

for i=1:length(dist)

eta=exp(-c*abs(dist(i)-dist));

discrim(i)=1/sum(eta);

end

%%Note: this could be vectorized for efficiency

plot(discrim,'-om')

axis([0 length(dist) 0 1])

xlabel('Serial Position','fontsize',14)

ylabel('Discriminability','fontsize',14)

set(gcf, 'color', 'white');

A Basis