This document provides an introduction to Hidden Markov Models (HMMs). It begins by explaining the key differences between Markov Models and HMMs, noting that in HMMs the states are hidden and can only be indirectly observed through observations. It then outlines the main elements of an HMM - the number of states, observations, state transition probabilities, observation probabilities, and initial state distribution. An example HMM is provided. Finally, it briefly introduces three common problems in HMMs - determining the most likely model given observations, determining the most likely state sequence, and determining the model parameters that are most likely to have generated the observations.
Aurelian Isar - Decoherence And Transition From Quantum To Classical In Open ...SEENET-MTP
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Aurelian Isar - Decoherence And Transition From Quantum To Classical In Open ...SEENET-MTP
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My talk in the MCQMC Conference 2016, Stanford University. The talk is about Multilevel Hybrid Split Step Implicit Tau-Leap
for Stochastic Reaction Networks.
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Presented at IEEE ICASSP-2007:
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Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
My talk in the MCQMC Conference 2016, Stanford University. The talk is about Multilevel Hybrid Split Step Implicit Tau-Leap
for Stochastic Reaction Networks.
WAVELET-PACKET-BASED ADAPTIVE ALGORITHM FOR SPARSE IMPULSE RESPONSE IDENTIFI...bermudez_jcm
Presented at IEEE ICASSP-2007:
This paper proposes a wavelet-packet-based (WPB) algorithm for efficient identification of sparse impulse responses with arbitrary frequency spectra. The discrete wavelet packet transform (DWPT) is adaptively tailored to the energy distribution of the unknown system\'s response spectrum. The new algorithm leads to a reduced number of active coefficients and to a reduced computational complexity, when compared to competing wavelet-based algorithms. Simulation results illustrate the applicability of the proposed algorithm.
z-Transform is for the analysis and synthesis of discrete-time control systems.The z transform in discrete-time systems play a similar role as the Laplace transform in continuous-time systems
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This lecture provides an overview on Markov processes and Hidden Markov Models. We will start off by going through a basic conceptual example and then explore the types of problems that can be solved with HMM's. The underlying algorithms will be discussed in detail with a quantitative focus and then we will conclude with a practical example concerning stock market prediction which highlights the techniques.
Supervised Hidden Markov Chains.
Here, we used the paper by Rabiner as a base for the presentation. Thus, we have the following three problems:
1.- How efficiently compute the probability given a model.
2.- Given an observation to which class it belongs
3.- How to find the parameters given data for training.
The first two follow Rabiner's explanation, but in the third one I used the Lagrange Multiplier Optimization because Rabiner lacks a clear explanation about how solving the issue.
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Tutorial on Probabilistic Models of Time Series and Sequences. Hidden Markov Models. Linear Dynamical Systems. Forward/backward algorithm. Kalman Filtering. Kalman Smoothing. Viterbi algorithm. Baum-Welch algorithm. Learning HMM. Learning LDS.
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Lecture by dr Cosmin Crucean (Theoretical and Applied Physics, West University of Timisoara, Romania) on July 9, 2010 at the Faculty of Science and Mathematics, Nis, Serbia.
2013.06.17 Time Series Analysis Workshop ..Applications in Physiology, Climat...NUI Galway
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The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
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https://www.rttsweb.com/jmeter-integration-webinar
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https://alandix.com/academic/papers/synergy2024-epistemic/
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Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
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The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
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Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
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Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
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But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
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https://arxiv.org/abs/2306.08302
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During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
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- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
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3. Markov Model
• Given 3 weather states:
– {S1, S2, S3} = {rain, cloudy, sunny}
Rain Cloudy Sunny
Rain 0.4 0.3 0.3
Cloudy 0.2 0.6 0.2
Sunny 0.1 0.1 0.8
• What is the probabilities for next 7 days
will be {sun, sun, rain, rain, sun, cloud,
sun} ?
4. Hidden Markov Model
• The states
– We don’t understand, Hidden!
– But it can be indirectly observed
• Example
– 北極or赤道(model), Hot/Cold(state), 1/2/3
ice cream(observation)
5. Hidden Markov Model
• The observation is a probability function
of state which is not observable directly
Hidden States
6. HMM Elements
• N, the number of states in the model
• M, the number of distinct observation
symbols
• A, the state transition probability distribution
• B, the observation symbol probability
distribution in states
• π, the initial state distribution λ: model
15. Forward Algorithm
• Initialization:
α1 (i ) = π i bi (O1 ) 1 ≤ i ≤ N
• Induction:
N 1 ≤ t ≤ T −1
αt +1 ( j ) = ∑αt ( i ) aij bj ( Ot +1 ) 1 ≤ j ≤ N
i=1
• Termination:
N
P(O | λ ) = ∑ αT (i )
i =1
16. Backward Algorithm
• Forward Algorithm
at (i ) = P(O1 , O2 ,..., Ot , qt = Si | λ )
• Backward Algorithm
– 給定時間 t 時狀態為 Si 的條件下,向後 向後局
向後
部觀察序列為 Ot+1, Ot+2, …, OT的機率
βt (i ) = P(Ot +1 , Ot + 2 ,..., OT , qt = Si | λ )
17. Backward Algorithm
• Initialization
βT (i ) = 1 1 ≤ i ≤ N
• Induction
N
t = T −1, T − 2, ...,1
βt (i ) = ∑ aij b j (Ot +1 ) β t +1 ( j )
j =1 1≤ i ≤ N
18. Backward Algorithm
R1 R1 R1
S1 S1 S1
R2 R2 R2
When OT = R1
S2 R1 S2 R1 S2 R1
R2 R2 R2
S3 R1 S3 R1 S3 R1
R2 R2 R2
1 2 3 t
N
β T −1 (1) = ∑ a1 j b j ( OT ) β T ( j )
j =1
= a11b1 ( OT ) + a12 b2 ( OT ) + a13b3 ( OT )
20. Solution 2
• 例: Choose the state qt which are individually
most likely
– γt(i) : the probability of being in state Si at
time t, given the observation sequence O,
and the model λ
P (O | qt = Si , λ ) α t ( i ) βt ( i ) α t ( i ) βt ( i )
γ t (i ) = = = N
P (O λ ) P (O λ )
∑ α t ( i ) βt ( i )
i =1
qt = argmax γ t ( i ) 1 ≤ t ≤ T
1≤i ≤ N
21. Viterbi algorithm
• The most widely used criteria is to find
the “single best state sequence”
maxmize P ( Q | O, λ ) ≈ maxmize P ( Q, O | λ )
• A formal technique exists, based on
dynamic programming methods, and is
called the Viterbi algorithm
22. Viterbi algorithm
• To find the single best state sequence, Q =
{q1, q2, …, qT}, for the given observation
sequence O = {O1, O2, …, OT}
• δt(i): the best score (highest prob.) along a
single path, at time t, which accounts for the
first t observations and end in state Si
δ t ( i ) = max P q1 q2 ... qt = Si , O1 O2 ... Ot λ
1 q , q ,..., q
2 t −1
23. Viterbi algorithm
• Initialization - δ1(i)
– When t = 1 the most probable path to a
state does not sensibly exist
– However we use the probability of being in
that state given t = 1 and the observable
state O1
δ1 ( i ) = π i bi ( O1 ) 1 ≤ i ≤ N
ψ (i ) = 0
24. Viterbi algorithm
• Calculate δt(i) when t > 1
– δt(i) : The most probable path to the state X
at time t
– This path to X will have to pass through one
of the states A, B or C at time (t-1)
Most probable path to A: δ t −1 ( A) a AX bX ( Ot )
25. Viterbi algorithm
• Recursion
δ t ( j ) = max δ t −1 ( i ) aij b j ( Ot )
2≤t ≤T
1≤ i ≤ N
ψ t ( j ) = argmax δ t −1 ( i ) aij 1≤ j ≤ N
1≤ i ≤ N
• Termination
P* = max δ T ( i )
1≤i ≤ N
q = argmax δ T ( i )
*
T
1≤i ≤ N
26. Viterbi algorithm
• Path (state sequence) backtracking
qt* = ψ t +1 (qt*+1 ) t = T − 1, T − 2, ..., 1
qT −1 = ψ T (qT ) = argmax δ T −1 ( i ) aiq*
* *
1≤i ≤ N T
...
...
* *
q1 = ψ 2 (q2 )
27. Solution 3
• 怎樣的模型 λ = (A, B, π) 最有可能產生
觀察到的現象
what 模型 maximize P(觀察到的現象|
模型)
• There is no known analytic solution. We
can choose λ = (A, B, π) such that P(O| λ)
is locally maximized using an iterative
procedure
28. Baum-Welch Method
• Define ξt(i, j) = P(qt=Si , qt+1=Sj|O, λ)
– The probability of being in state Si at time t,
and state Sj at time t+1
α t ( i ) aij b j ( Ot +1 ) βt +1 ( j )
ξt ( i, j ) =
P (O λ )
α t ( i ) aij b j ( Ot +1 ) βt +1 ( j )
= N N
∑∑ α ( i ) a b ( O ) β ( j )
i =1 j =1
t ij j t +1 t +1
29. Baum-Welch Method
• γt(i) : the probability of being in state Si at time
t, given the observation sequence O, and the
model λ
α t ( i ) βt ( i ) α ( i ) βt ( i )
γ t (i ) = = N t
P (O λ )
∑ α t ( i ) βt ( i )
• Relate γt(i) to ξt(i, j) i =1
α t ( i ) aij b j ( Ot +1 ) βt +1 ( j )
N ξt ( i, j ) =
γ t ( i ) = ∑ ξt ( i, j ) P (O λ )
j =1 α t ( i ) aij b j ( Ot +1 ) βt +1 ( j )
= N N
∑∑ α ( i ) a b ( O ) β ( j )
i =1 j =1
t ij j t +1 t +1
30. Baum-Welch Method
• The expected number of times that state Si is
visited
T −1
∑ γ ( i ) = Expected number of transitions from Si
t =1
t
• Similarly, the expected number of transitions
from state Si to state Sj
T −1
∑ ξ ( i, j ) = Expected number of transitions from S to S
t =1
t i j
31. Baum-Welch Method
• Re-estimation formulas for π, A and B
π i = γ1(i)
T −1
∑ξ (i, j)
t =1
t
expected number of transitions from state Si to S j
aij = T −1
=
expected number of transitions from state Si
∑γt (i)
t =1
T
∑t =1
γ t ( j)
s.t. Ot =vk expected number of times in state j and observing symbol vk
b j (k) = T
=
expected number of times in state j
∑γ ( j)
t =1
t
32. Baum-Welch Method
• P(O|λ) > P(O|λ)
• Iteratively use λ in place of λ and repeat
the re-estimation, we then can improve
P(O| λ) until some limiting point is
reached