The document describes various probability distributions that can arise from combining Bernoulli random variables. It shows how a binomial distribution emerges from summing Bernoulli random variables, and how Poisson, normal, chi-squared, exponential, gamma, and inverse gamma distributions can approximate the binomial as the number of Bernoulli trials increases. Code examples in R are provided to simulate sampling from these distributions and compare the simulated distributions to their theoretical probability density functions.
ゼロから始める深層強化学習(NLP2018講演資料)/ Introduction of Deep Reinforcement LearningPreferred Networks
Introduction of Deep Reinforcement Learning, which was presented at domestic NLP conference.
言語処理学会第24回年次大会(NLP2018) での講演資料です。
http://www.anlp.jp/nlp2018/#tutorial
本スライドは、弊社の梅本により弊社内の技術勉強会で使用されたものです。
近年注目を集めるアーキテクチャーである「Transformer」の解説スライドとなっております。
"Arithmer Seminar" is weekly held, where professionals from within and outside our company give lectures on their respective expertise.
The slides are made by the lecturer from outside our company, and shared here with his/her permission.
Arithmer株式会社は東京大学大学院数理科学研究科発の数学の会社です。私達は現代数学を応用して、様々な分野のソリューションに、新しい高度AIシステムを導入しています。AIをいかに上手に使って仕事を効率化するか、そして人々の役に立つ結果を生み出すのか、それを考えるのが私たちの仕事です。
Arithmer began at the University of Tokyo Graduate School of Mathematical Sciences. Today, our research of modern mathematics and AI systems has the capability of providing solutions when dealing with tough complex issues. At Arithmer we believe it is our job to realize the functions of AI through improving work efficiency and producing more useful results for society.
ゼロから始める深層強化学習(NLP2018講演資料)/ Introduction of Deep Reinforcement LearningPreferred Networks
Introduction of Deep Reinforcement Learning, which was presented at domestic NLP conference.
言語処理学会第24回年次大会(NLP2018) での講演資料です。
http://www.anlp.jp/nlp2018/#tutorial
本スライドは、弊社の梅本により弊社内の技術勉強会で使用されたものです。
近年注目を集めるアーキテクチャーである「Transformer」の解説スライドとなっております。
"Arithmer Seminar" is weekly held, where professionals from within and outside our company give lectures on their respective expertise.
The slides are made by the lecturer from outside our company, and shared here with his/her permission.
Arithmer株式会社は東京大学大学院数理科学研究科発の数学の会社です。私達は現代数学を応用して、様々な分野のソリューションに、新しい高度AIシステムを導入しています。AIをいかに上手に使って仕事を効率化するか、そして人々の役に立つ結果を生み出すのか、それを考えるのが私たちの仕事です。
Arithmer began at the University of Tokyo Graduate School of Mathematical Sciences. Today, our research of modern mathematics and AI systems has the capability of providing solutions when dealing with tough complex issues. At Arithmer we believe it is our job to realize the functions of AI through improving work efficiency and producing more useful results for society.
Создание картограмм на принципах грамматики графики. С помощью R-расширения g...Matrunich Consulting
Слайды выступления Александра Матрунича на конференции "Открытые ГИС" 17 ноября 2012 г. в Москве.
Грамматика графики - подход к визуализации статистических данных, позволяющий перейти к содержательной части графика и не отвлекаться второстепенные детали, которые создаются автоматически. Ggplot2 - расширение Хэдли Викхэма для среды статистической обработки данных R, реализующее концепцию грамматики графики. Для создания графика в ggplot2 пользователь указывает исходный массив данных, сопоствляет переменным из массива подходящие средства графического представления (такими могут быть положение по вертикали и горизонтали, размер, цвет заливки, цвет обводки, форма и др.), выбирает тип геометрического объекта (например, точка, прямоугольник, линия, изолиния, ящик с усами и пр.), и при необходимости устанавливает способ статистического преобразования данных, тип координатной системы.
Ggmap - расширение Дэвида Кахли для R, "заточенное" под создание картограмм и основанное на ggplot2. В качестве положения по вертикали и горизонтали в ggmap зафиксированы широта и долгота, в качестве проекции - Меркатор. Ggmap упрощает процесс визуализации пространственных данных, минимизируя усилия пользователя под установке географической подложки для своего графика. В качестве подложки могут быть выбраны слои из сервиса Google Maps, OpenStreetMap, CloudMade.
Show drafts
volume_up
Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
From intelligent search and recommendations to automated data productisation and quotation, Opendatabay AI-driven features streamline the data workflow. Finding the data you need shouldn't be a complex. Opendatabay simplifies the data acquisition process with an intuitive interface and robust search tools. Effortlessly explore, discover, and access the data you need, allowing you to focus on extracting valuable insights. Opendatabay breaks new ground with a dedicated, AI-generated, synthetic datasets.
Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
157. xi µ
p
n
xi µ
p
n
Mxi µ
p
n
(t) = E[e
xi µ
p
n
t
]
= 1 + 2 t2
2!n
+ µ3
t3
3!n3/2
+ · · · + µk
tk
k!nk/2
+ · · ·
= 1 +
2
t2
2n
+
n
2n
=
1
2n
n n ! 0 n ! 0
= 1 +
2
t2
+ n
2n
158. T0
=
x1 µ
p
n
+
x2 nµ
p
n
+ · · · +
xn µ
p
n
=
nX
i=1
xi µ
p
n
MT 0 (t) = MPn
i=1
⇣
xi µ
p
n
⌘(t) = E[e
Pn
i=1
⇣
xi µ
p
n
⌘
t
]
=
nY
i=0
E[e
⇣
xi µ
p
n
⌘
t
] =
✓
1 +
1
n
2
t2
+ n
2
◆n
er
⌘ lim
n!1
⇣
1 +
r
n
⌘n
r
r
= lim
n!1
⇣
1 +
r
n
⌘n
159. n ! 1
lim
n!1
MT 0 = lim
n!1
✓
1 +
1
n
2
t2
+ n
2
◆n
= e
2t2
2
lim
n!1
n = 0
N(0, 2
)
T0
=
T nµ
p
n
2
185. u ⇠ N(0, 1)
t =
u
p
v/m
v ⇠ 2
(m)
f(t) =
m+1
2
p
m⇡ m
2
✓
t2
m
+ 1
◆ m+1
2
186. u ⇠ N(0, 1) v ⇠ 2
(m) v > 01 < u < +1
f(u, v) =
1
p
2⇡
exp
✓
u2
2
◆
(1/2)n/2
(n/2)
vn/2 1
e v/2
t =
u
p
v/m
x = v
f(t) =
m+1
2
p
m⇡ m
2
✓
t2
m
+ 1
◆ m+1
2
(z) =
Z 1
0
tz 1
e t
dt
187. µ
D = (x1, · · · , xn) xi ⇠ N(µ, 2
)
¯x ⇠ N(µ, 2
/n)¯x
1
2
nX
i=1
(xi ¯x)2
⇠ 2
n 1
188. u =
¯x µ
/
p
n
⇠ N(0, 1) v =
1
2
nX
i=1
(xi ¯x)2
⇠ 2
n 1
t =
u
p
v/(n 1)
=
¯x µ
/
p
n
·
"
1
2
1
(n 1)
nX
i=1
(xi ¯x)2
# 1/2
=
¯x µ
1/
p
n
·
1
p
s2
=
¯x µ
s/
p
n
⇠ tn 1
s2
=
1
n 1
nX
i=1
(xi ¯x)2
s2
189. P
✓
tn 1;↵/2 5
¯x µ
s/
p
n
5 tn 1;↵/2
◆
= 1 ↵
tn 1;↵/2 tn 1;↵/2
↵/2 ↵/2
1 ↵
1 ↵
1 ↵
P
✓
¯x tn 1;↵/2
s
p
n
5 µ 5 ¯x + tn 1;↵/2
s
p
n
◆
= 1 ↵
[ tn 1;↵/2, tn 1;↵/2]
µ
1 ↵
190. P
✓
tn 1;↵/2 5
¯x µ
s/
p
n
5 tn 1;↵/2
◆
= 1 ↵
tn 1;↵/2 tn 1;↵/2
↵/2 ↵/2
1 ↵
1 ↵
1 ↵
P
✓
¯x tn 1;↵/2
s
p
n
5 µ 5 ¯x + tn 1;↵/2
s
p
n
◆
= 1 ↵
[ tn 1;↵/2, tn 1;↵/2]
µ
1 ↵