Read "Streaming Systems" 1&2, Streaming 101 Read "F1, a distributed SQL database that scales" Read "Zanzibar, Google’s Consistent, Global Authorization System" Read "Spanner, Google's Globally-Distributed Database" Read "Designing Data-intensive applications" 12, The Future of Data Systems IOS development with Swift Read "Designing Data-intensive applications" 10&11, Batch and Stream Processing Read "Designing Data-intensive applications" 9, Consistency and Consensus Read "Designing Data-intensive applications" 8, Distributed System Troubles Read "Designing Data-intensive applications" 7, Transactions Read "Designing Data-intensive applications" 6, Partitioning Read "Designing Data-intensive applications" 5, Replication Read "Designing Data-intensive applications" 3&4, Storage, Retrieval, Encoding Read "Designing Data-intensive applications" 1&2, Foundation of Data Systems Three cases of binary search TAMU Operating System 2 Memory Management TAMU Operating System 1 Introduction Overview in cloud computing 2 TAMU Operating System 7 Virtualization TAMU Operating System 6 File System TAMU Operating System 5 I/O and Disk Management TAMU Operating System 4 Synchronization TAMU Operating System 3 Concurrency and Threading TAMU Computer Networks 5 Data Link Layer TAMU Computer Networks 4 Network Layer TAMU Computer Networks 3 Transport Layer TAMU Computer Networks 2 Application Layer TAMU Computer Networks 1 Introduction Overview in distributed systems and cloud computing 1 A well-optimized Union-Find implementation, in Java A heap implementation supporting deletion TAMU Advanced Algorithms 3, Maximum Bandwidth Path (Dijkstra, MST, Linear) TAMU Advanced Algorithms 2, B+ tree and Segment Intersection TAMU Advanced Algorithms 1, BST, 2-3 Tree and Heap TAMU AI, Searching problems Factorization Machine and Field-aware Factorization Machine for CTR prediction TAMU Neural Network 10 Information-Theoretic Models TAMU Neural Network 9 Principal Component Analysis TAMU Neural Network 8 Neurodynamics TAMU Neural Network 7 Self-Organizing Maps TAMU Neural Network 6 Deep Learning Overview TAMU Neural Network 5 Radial-Basis Function Networks TAMU Neural Network 4 Multi-Layer Perceptrons TAMU Neural Network 3 Single-Layer Perceptrons Princeton Algorithms P1W6 Hash Tables & Symbol Table Applications Stanford ML 11 Application Example Photo OCR Stanford ML 10 Large Scale Machine Learning Stanford ML 9 Anomaly Detection and Recommender Systems Stanford ML 8 Clustering & Principal Component Analysis Princeton Algorithms P1W5 Balanced Search Trees TAMU Neural Network 2 Learning Processes TAMU Neural Network 1 Introduction Stanford ML 7 Support Vector Machine Stanford ML 6 Evaluate Algorithms Princeton Algorithms P1W4 Priority Queues and Symbol Tables Stanford ML 5 Neural Networks Learning Princeton Algorithms P1W3 Mergesort and Quicksort Stanford ML 4 Neural Networks Basics Princeton Algorithms P1W2 Stack and Queue, Basic Sorts Stanford ML 3 Classification Problems Stanford ML 2 Multivariate Regression and Normal Equation Princeton Algorithms P1W1 Union and Find Stanford ML 1 Introduction and Parameter Learning

TAMU Neural Network 2 Learning Processes

2017-01-26

  1. five basic learning rules
    • error correction
    • Hebbian
    • memory-based
    • competitive
    • Boltzmann
  2. learning paradigms
    • credit assignment problem
    • supervised learning
    • unsupervised learning
  3. learning tasks, memory and adaptation
  4. probabilistic and statistical aspects of learning

learning rules

error-correction learning

tamu-nn-slide2-error

  • input , output and desired response or target output
  • error signal
  • actuates a control mechanism that gradually adjust the synaptic weights, to minimize the cost function (or index of performance)
    • cost function:
  • when synaptic weights reach a steady state, learning is stopped.

  • Widrow-Hoff rule, with learning rate :
  • With that, we can update the weights:

memory-based learning

  • All (or most) past experiences are explicitly stored, as input-target pairs
  • Two classes
  • Given a new input , determine class based on local neighborhood of .
    • Criterion used for determining the neighborhood
    • Learning rule applied to the neighborhood of the input, within the set of training examples.

nearest neighbor

Nearest neighbor of :
\[min_i d(x_i,x_{test}) = d(x_N’,x_{test})\]
where is the Euclidean distance.

  • is classified as the same class as

k-nearest neighbor

  • Identify k classified patterns that lie nearest to the test vector , for some integer k.
  • Assign to the class that is most frequently represented by the k neighbors (use majority vote)
  • In effect, it is like averaging. It can deal with outliers

Hebbian Learning

  • If two neurons on either side of a synapse are activated simultaneously, the synapse is strengthened.
  • If they are activate asynchronously, the synapse is weekened or eliminated.

tamu-nn-slide2-hebbian

Hebbian learning with learning rate :
Covariance rule:

covariance rule

  • convergence to a nontrivial state
  • prediction of both potentiation and depression
  • observations
    • weight enhanced when both pre- and post-synaptic activities are above average
    • weight depressed when
      • pre- more than average, post- less than average
      • pre- less than average, post- more than average

competitive learning

  • Output neurons compete with each other for a chance to become active.
  • Highly suited to discover statistically salient features (that may aid in classification)
  • three basic elements:
    • Same type of neurons with different weight sets, so that they respond differently to a given set of inputs
    • A limit imposed on strength of each neuron
    • Competition mechanism, to choose one winner: winner-takes-all neuron.

\[\Delta w_{kj} = \eta (x_j-w_{kj}), \mbox{ if } k \mbox{ is the winner}\]

tamu-nn-slide2-compete

Synaptic weight vector is moved toward the input vector.
Weight vectors converge toward local input clusters: clustering

Boltzmann Learning

  • Stochastic learning algorithm rooted in statistical mechanics
  • Recurrent network, binary neurons (+1 or -1)
  • Energy function
  • Activation:
    • Choose a random neuron k
    • Flip state with a probability (given temperature T)
      • \[P(x_k \rightarrow -x_k) = (1+exp(-\Delta E_k/T))^{-1}\]
      • is the change in E due to the flip

Boltzmann Machine

Types of neurons

  • Visible: can be affected by the environment
  • Hidden: isolated

Types of operations

  • Clamped: visible neurons are fixed by environmental input and held constant
  • Free-running: all neurons update their activity freely.

  • Learning
    • update weight during both clamped and free running condition
  • Train weight with various clamping input patterns
  • After training is completed, present new clamping input pattern that is a partial input of one of the known vectors
  • Let it run clamped on the new input (subset of visible neurons), and eventually it will complete the pattern

Learning Paradigms

credit assignment

Assign credit or blame for overall outcome to individual decisions.

  • for outcomes of actions
  • for actions to internal decisions

learning with a teacher

learning without a teacher

two classes

  • reinforcement learning/neurodynamic programming
  • unsupervised learning/self-organization

reinforcement

Goal is optimize the cumulative cost of actions.
In many cases, learning is under delayed reinforcement.

unsupervised

Based on task-independent measure

learning tasks, memory and adaptation

pattern association

Associate key pattern with memorized pattern.

pattern classification

Mapping between input pattern and a prescribled number of classes.

function approximation

Nolinear input-output mapping.
System identification: learn function of an unknown system

control

Control a plant, adjust plant input u so that the output of the plant y tracks the reference signal d.

filtering/beamforming

Filtering: estimate quantity at time n, based on measurements up to time n
smoothing: estimate quantity at time n, based on measurements up to time n+a
prediction: estimate quantity at time n+a, based on measurements up to time n

memory

q pattern pairs :
Input (key) vector:
Output (memorized) vector:
By a weight matrix:
\[y_k = W(k)x_k\]

Let
\[M = \sum_{k=1}^{q} W(k)=\sum_{k=1}^{q} y_k x_k^T\]
If all are nomalized to length 1, then:
\[M x_j = y_j\]

adaptation

  • stationary environment: supervised learning can be used to obtain a relatively stable set of parameters
  • nonstationary environment: parameters need to be adapted over time
  • locally stationary

statistical nature of learning

Target function:

Neural network realization of the function: or

Random input vectors and random output scalar values

Training set:

regressive model:

Error term has zero mean:

\[E[D \vert x] = f(x)\]

\[E[\epsilon f(X)] = 0\]

Cost function:
\[\mathcal{E}(w)= \frac{1}{2}\sum_{i=1}^{N}(d_i - F(x_i,w))^2\]
\[\mathcal{E}(w)= \frac{1}{2}E_T[\epsilon^2] + E_T[\epsilon(f(x)-F(x,T))]+\frac{1}{2}E_T[(f(x)-F(x,T))^2]\]

The first term is intrinsic error; second reduces to 0; we are interested in the third term.

bias and variance

  • bias: how much differs from the true function , approximation error
  • variance: the variance in over entire training set , estimation error

VC dimension

Vapnik-Chervonenkis

Shattering: a dichotomy of a set S is a partition of S into two disjoint subsets.

A set of instances S is shattered by a function class if and only if for every dichotomy of S there exists some function in consistent with this dichotomy.

The VC dimension is the size of the largest finite subset shattered by that function.

At least one subset of a size can be shattered, then this size can be shattered by that .

If is a set of lines,

VC dimension increases:

  • Training error decreases
  • confidence interval increases
  • sample complexity increases

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