This document provides an overview of variational inference (VI), a class of algorithms used to approximate intractable posterior distributions. VI frames Bayesian inference as an optimization problem where the goal is to find the distribution Q that minimizes the Kullback-Leibler divergence between Q and the true posterior P. Mean field theory and coordinate ascent variational inference (CAVI) are introduced as approaches for simplifying the variational distribution Q. Stochastic VI is also discussed as a method for scaling VI to large datasets. Examples of using VI for Gaussian and latent Dirichlet allocation models are provided.
In this talk, we discuss some recent advances in probabilistic schemes for high-dimensional PIDEs. It is known that traditional PDE solvers, e.g., finite element, finite difference methods, do not scale well with the increase of dimension. The idea of probabilistic schemes is to link a wide class of nonlinear parabolic PIDEs to stochastic Levy processes based on nonlinear version of the Feynman-Kac theory. As such, the solution of the PIDE can be represented by a conditional expectation (i.e., a high-dimensional integral) with respect to a stochastic dynamical system driven by Levy processes. In other words, we can solve the PIDEs by performing high-dimensional numerical integration. A variety of quadrature methods could be applied, including MC, QMC, sparse grids, etc. The probabilistic schemes have been used in many application problems, e.g., particle transport in plasmas (e.g., Vlasov-Fokker-Planck equations), nonlinear filtering (e.g., Zakai equations), and option pricing, etc.
In this talk, we discuss some recent advances in probabilistic schemes for high-dimensional PIDEs. It is known that traditional PDE solvers, e.g., finite element, finite difference methods, do not scale well with the increase of dimension. The idea of probabilistic schemes is to link a wide class of nonlinear parabolic PIDEs to stochastic Levy processes based on nonlinear version of the Feynman-Kac theory. As such, the solution of the PIDE can be represented by a conditional expectation (i.e., a high-dimensional integral) with respect to a stochastic dynamical system driven by Levy processes. In other words, we can solve the PIDEs by performing high-dimensional numerical integration. A variety of quadrature methods could be applied, including MC, QMC, sparse grids, etc. The probabilistic schemes have been used in many application problems, e.g., particle transport in plasmas (e.g., Vlasov-Fokker-Planck equations), nonlinear filtering (e.g., Zakai equations), and option pricing, etc.
Variational inference is a technique for estimating Bayesian models that provides similar precision to MCMC at a greater speed, and is one of the main areas of current research in Bayesian computation. In this introductory talk, we take a look at the theory behind the variational approach and some of the most common methods (e.g. mean field, stochastic, black box). The focus of this talk is the intuition behind variational inference, rather than the mathematical details of the methods. At the end of this talk, you will have a basic grasp of variational Bayes and its limitations.
Variational inference is a technique for estimating Bayesian models that provides similar precision to MCMC at a greater speed, and is one of the main areas of current research in Bayesian computation. In this introductory talk, we take a look at the theory behind the variational approach and some of the most common methods (e.g. mean field, stochastic, black box). The focus of this talk is the intuition behind variational inference, rather than the mathematical details of the methods. At the end of this talk, you will have a basic grasp of variational Bayes and its limitations.
In this presentation we describe the formulation of the HMM model as consisting of states that are hidden that generate the observables. We introduce the 3 basic problems: Finding the probability of a sequence of observation given the model, the decoding problem of finding the hidden states given the observations and the model and the training problem of determining the model parameters that generate the given observations. We discuss the Forward, Backward, Viterbi and Forward-Backward algorithms.
We consider the problem of model estimation in episodic Block MDPs. In these MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are interested in estimating the latent state decoding function (the mapping from the observations to latent states) based on data generated under a fixed behavior policy. We derive an information-theoretical lower bound on the error rate for estimating this function and present an algorithm approaching this fundamental limit. In turn, our algorithm also provides estimates of all the components of the MDP.
We apply our results to the problem of learning near-optimal policies in the reward-free setting. Based on our efficient model estimation algorithm, we show that we can infer a policy converging (as the number of collected samples grows large) to the optimal policy at the best possible asymptotic rate. Our analysis provides necessary and sufficient conditions under which exploiting the block structure yields improvements in the sample complexity for identifying near-optimal policies. When these conditions are met, the sample complexity in the minimax reward-free setting is improved by a multiplicative factor $n$, where $n$ is the number of contexts.
I am using DL & Actor critic tools for solving Variational inference problem. The intriguing part from my hand is that the likelihood has a Beta distribution.Thus we handle both VI issues and a non common distributions
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
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
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
JMeter webinar - integration with InfluxDB and GrafanaRTTS
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
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
2. Framework –Bayesian Inference
• The inputs:
1. Sample of length n (numbers, categories, vectors, images)
We denote this entity–Evidence
2. An assumption about the probabilistic structure that generates the sample –Hypothesis
Posterior =P(H|E)
Objective : GainUpdate information about the Hypothesis using the Evidence
3. Bayesian Inference- into formulas
• Estimating hypothesis upon the evidence:
• Z,X random variables
We wish to have P(Z|X) .
• Bayes formula:
P(Z|X) =
𝑃(𝑍,𝑋)
𝑃(𝑋)
Bayesian inference is therefore about working with the RHS terms.
4. RHS terms
• Hidden Variables (Hypothesis)(Z)- The variables of the mechanism that
generates the sample
(e.g. topics distribution in a corpus or the Gaussians in GMM)
1. The values are not given
2. We have the joint distribution P(Z,X) !!!
• Observed Data (Evidence) (X)- The sample that we actually have.
1. We know every value
2. We may know nothing about its distribution
5. RHS terms (Cont.)
• In some case studies P(X) is intractable or extremely difficult to
calculate.
• We cannot obtain the conditional distribution based on Bayes
formula’s terms
• Variational inference offers a class of algorithms to solve this
problem: Approximating posterior for difficult P(X)
6. Examples:
GMM (Known # Gaussian & Variance)
We have K Gaussians
Draw μ 𝑘 ~ 𝑁 0, τ (τ is positive)
For each sample j =1…n
𝑧𝑗 ~Cat (1/K,1/K…1/K)
𝑥𝑗 ~ 𝑁(μ 𝑧 𝑗
, σ)
p(𝑥1….𝑛) = μ1:𝑘 𝑙=1
𝐾
𝑃(μ𝑙) 𝑖=1
𝑛
𝑧 𝑗
𝑝( 𝑧𝑗) P(𝑥𝑖|μ 𝑧 𝑗
) => 𝑃𝑟𝑒𝑡𝑡𝑦 𝑆ℎ𝑖𝑡 !
7. Examples - LDA
Corpus D every document of length N
N ∼ Poisson(ξ)
θ ∼ Dir(α).
Β -Topics (array of words ,fixed or Dirichlet)
For each of the N words 𝑤 𝑛:
a topic 𝑧 𝑛 ∼ Cat(θ).
𝑤 𝑛 ~ p(𝑤 𝑛|𝑧 𝑛, β)
β𝑖𝑗 = P(𝑤𝑖|𝑧𝑗 )
p(w|α, β) = 𝑃(θ|α) 𝑖=1
𝑛
𝑧 𝑛
(p(𝑧 𝑛|θ)p(wn|𝑧 𝑛, β))dθ
8. Sampling
• The common solution for estimating distributions is sampling:
1. MCMC
• Metropolis-Hastings
• Gibbs
2 RBM –(Mostly by Gibbs sampling)
3. Hybrid Monte Carlo
• Today we wont talk about these methods!
9. Sampling Vs. Analysis
• Sampling
1. The solutions are exact
2. Numerically expensive
Deterministic
1. Solutions are cheaper
2. Less accurate
3. Non-conjugate problem
4. An optimization process
10. Sampling Vs. Analysis cont.
• MCMC methods are good for small data where accuracy is essential
• When we have big data and many modes should be tested ,VI
methods have an advantage
11. Can we do something analytically?
• Can we analytically approximate the posterior ?!
• Can we find a distribution that is closed to the posterior and well estimate the distance?
• When the framework is a vector space
1. Calculus –Allows us to find extremums easily
2. We are endowed with 𝐿 𝑃 metrics (typically p=1 , 2)
• Our domain is the functions space and their functional
We need:
1. An analytical method to find functional’s extremums
2. Nice metric
12. Calculus of Variations
• Consider the following
𝐹, 𝑦 functions-(with all the “extras”)
J(y)= 𝐹( 𝑦, 𝑦′
𝑡)𝑑𝑡 (𝑦 𝑖𝑠 𝑑𝑖𝑓𝑓. )
If y is an extremum of J it satisfies Euler-Lagrange eq.
𝑑𝐹
𝑑𝑦
-
𝑑
𝑑𝑡
(
𝑑𝐹
𝑑𝑦′
) = 0
• Example: maximum entropy principle
Generally speaking this domain is a calculus for functional spaces hence it is
beneficial for optimizations
13. Calculus of Var. Cont.
The fundamental lemma of Calculus of variations:
If M continuous, and for all h differentiable
𝑎
𝑏
𝑀 𝑥 ∗ ℎ 𝑥 = 0 ⟹ 𝑀 ≡ 0 on (a,b) (Chybenko)
Generally speaking this domain is a calculus for functional spaces hence
it is beneficial for optimizations
14. KL (Kullback-Leibler) Divergence
• A metric on distributions
* “On Information and Sufficiency” 1951 (Ann Math Statist)
Properties:
1. Non-symmetric (It actually measures a relative distance :which distribution
P observes as the closest)
1. Concave -> 0 is obtained only for Kl(p,p) (proof by concavity of log an Jensen Lagrange
multipliers))
2. The distance between P(x,y) to p(x) *p(y)=0
Usage:
Cross Entropy = H(p)+ KL(p,q)
15. PMI (Pointwise Mutual Information)
• Let X,Y random variables
• PMI(X,Y)=Log[
𝑃(𝑋=𝑎,𝑌=𝑏)
𝑃 𝑋=𝑎 𝑃(𝑌=𝑏)
]
• KL(p(X/Y=a),Q(x)) = 𝑥 𝑃(𝑋 = 𝑥|𝑌 = 𝑎)PMI(X=x, Y=a)
• What does this term mean?
16. ELBO- Evidence Lower Bound
Consider now P(X) –The Evidence
We have :
log(P(X)) ≥ 𝐸 𝑄 [log p(x, Z)] − 𝐸 𝑄 [log Q(Z)]
The RHS is called ELBO and it is a lower bound of the LHS
17. Back to KL
• Having the requested analytical tools we can approximate the
posterior: find Q s.t. Q(Z) ~ P(Z|X) :
• min(KL(Q(Z)||P(Z|X) )
KL(Q||P(Z|X) )= Log(P(X))- ELBO
=>Log(P(X)) = KL(Q||P(Z|X) ) +ELBO
P is fixed Hence: Maximizing ELBO =>minimizing KL
18. Let’s use Calculus!
• We wish to optimize the ELBO term.
We can define a functional :
𝐸𝐿𝐵𝑂 = 𝐸 𝑄[log p(X, Z)] − 𝐸 𝑄 [log Q(Z)] = 𝑄𝐿𝑜𝑔(
𝑃(𝑋,𝑍)
𝑄(𝑍)
)= J(Q)
We can go to Euler –Lagrange here, but let’s try and simplify Q!
19. Mean Field Theory-MFT
• The main idea is solving many-body problem (Ising model)
Assume system of many bodies (atoms ,other particles)
1. For each body replace its interaction particles with their average.
2. Assume no correlations between interacted bodies
We will use section 2 to simplify Q
Q(z) = 𝑖=1
𝑛
𝑞𝑖(𝑧𝑖) (Obviously not true)
20. MFT –cont.
• We can use now Euler –Lagrange with the constrain
𝑞𝑖(z) =1
• We obtain
L𝑜𝑔(𝑞𝑖) = 𝑐𝑜𝑛𝑠𝑡 + 𝐸−𝑖[𝑝 𝑥, 𝑧 ] Bolzman Dist.!
Did we win ? No!
Note that each 𝑞𝑖 may change other 𝑞 𝑗′ 𝑠
21. Coordinate Ascent Variational Inference
CAVI
• An iterative algorithm
1. Construct a model P(X,Z)
2. Set sequentially each 𝑞𝑖 to 𝐸−𝑖[𝑝 𝑥, 𝑧 ] +constant
3. As always we repeat until the q’s converge
(Wikipedia,Blei) https://www.youtube.com/watch?v=uKxtmkfeuxg
“Message passing” – Winn & Bishop
Minka 2005, Knowles & Minka 2011
23. Gaussian Cont.
• P(X|τ, μ) = 𝑖=1
𝑛
𝑁(𝑥 𝑛|τ, μ)
• P(μ| τ) = N(μ|μ0,(λ0τ)−1)
• P(τ)= 𝐺𝑎𝑚𝑚𝑎 (τ|𝑎0, 𝑏0)
• MFT implies:
q(μ, τ ) = 𝑞 μ 𝑞 τ (Not that accurate in this case !)
Using ELBO formula:
Ln(𝑞 μ )= 𝐸τ[ln(P(X|τ, μ))+ln(P(μ| τ) +ln(P(τ))]+C
Ln(𝑞 τ )= 𝐸μ[ln(P(X|τ, μ))+ln(P(μ| τ) +ln(P(τ))]+C
24. Stochastic - VI
• CAVI does not work well for big data (update for every item)
• Stochastic VI- rather updating the q’s, we calculate the gradient of the
ELBO, and optimize its parameters (similar to EM)
• Used in LDA applications (David Blei et al)
• http://www.columbia.edu/~jwp2128/Papers/HoffmanBleiWangPaisle
y2013.pdf
• https://www.cs.princeton.edu/courses/archive/fall11/cos597C/readin
g/Blei2011.pdf
•
25. Appendix- Ising Model
• Ferromagnetism (Pierre Weiss )
• Ising Model -Lenz & Ernst Ising
• We have a Hamiltonian
H (σ) = -h 𝑥 𝜎𝑥 − 𝑗 𝑦𝑥 𝜎𝑥 𝜎 𝑦
(𝜎𝑥 -the spin of a site (atom) y,x are nearest neighbors hence the sum is over
adjacent spins, h is the magnetic field and j is the “coupling constant”)
• Consider the contribution of a single atom (spin):
ξ(𝜎𝑥) = -h𝜎𝑥 -j𝜎𝑥 𝑦 𝜎 𝑦
(y runs over the near spins of x)
26. Ising Model(cont.)
• Now we replace the second summation by its mean :
ξ(𝜎𝑥) = -h𝜎𝑥 - j𝜎𝑥 < 𝜎 𝑦 > We obtain
ξ(𝜎𝑥) = −ℎ0 𝜎𝑥
• Note that if we are use this approximation to average the entire
system we can use this approximation to have:
𝐸 𝑚𝑓 =𝐸0-h 𝑥 𝜎𝑥
The solution single Bolzman spin dist.:
P(𝑠𝑖) = 𝑒 𝑎∗𝑠 𝑖 /(𝑒 𝑎∗𝑠 𝑖 +𝑒−𝑎∗𝑠 𝑖)
27. Remarks
1 Maxwell speeds – The use of independency for “achieving” normal
distribution
2 RBM
3 Conditional Random Field (CRF)
4. Cybenko., G. (1989) "Approximations by superposition of sigmoidal
functions“
5. Kullback & Leibler “On Information and Sufficiency”
6. David Blei – Latent Dirichlet Allocations (and the rest of his papers)
7. Expected maximization algorithm (EM, Baum-Welch)
29. VI –Other Languages.
• R- https://artax.karlin.mff.cuni.cz/r-help/library/varbvs/html/00Index.html
• R - https://cran.r-project.org/web/packages/varbvs/varbvs.pdf
• R - https://github.com/kieranrcampbell/clvm (claim that they implement
CAVI )
• Blog on Scala http://alexminnaar.com/online-latent-dirichlet-allocation-
the-best-option-for-topic-modeling-with-large-data-sets.html
• Spark mllib -
https://github.com/apache/spark/blob/master/mllib/src/main/scala/org/a
pache/spark/mllib/clustering/LDAOptimizer.scala