Канал: Dr Mihai Nica

Counterintuitive Coin Flips meet Deep Neural Network Theory

Counterintuitive Coin Flips meet Deep Neural Network Theory

Putnam Probability Picture Proof | Putnam 1989 A4

Putnam Probability Picture Proof | Putnam 1989 A4

"Infinite Monkeys Theorem" Challenged?

"Infinite Monkeys Theorem" Challenged?

Probability's "Darth Vader Rule" with Manim Tutorial Live Coding

Probability's "Darth Vader Rule" with Manim Tutorial Live Coding

"A Random Variable is NOT Random and NOT a Variable"

"A Random Variable is NOT Random and NOT a Variable"

Find and Fix Random Errors the Easy Way: Hamming(7,4)

Find and Fix Random Errors the Easy Way: Hamming(7,4)

3 New Random Variable Identities a la 3Blue1Brown's Probability Challenge

3 New Random Variable Identities a la 3Blue1Brown's Probability Challenge

3Blue1Brown's Probability Challenge Solved!

3Blue1Brown's Probability Challenge Solved!

Fibonacci Converts miles to km the Fun Way #SoMEpi

Fibonacci Converts miles to km the Fun Way #SoMEpi

The Coin Flip Game that Stumped Twitter: Alice HH vs Bob HT

The Coin Flip Game that Stumped Twitter: Alice HH vs Bob HT

Business Math - Intro to the course [ LECTURE RECORDING ] MATH1030 - See playlist in description

Business Math - Intro to the course [ LECTURE RECORDING ] MATH1030 - See playlist in description

The Math of "The Trillion Dollar Equation"

The Math of "The Trillion Dollar Equation"

[Lecture] Monte Carlo evaluation and control: A Gridworld Example | Intro to Markov Chains and RL

[Lecture] Monte Carlo evaluation and control: A Gridworld Example | Intro to Markov Chains and RL

[Lecture] Is it safe to differentiate under the integral? Lebesgue Dominated Convergence theorem

[Lecture] Is it safe to differentiate under the integral? Lebesgue Dominated Convergence theorem

[ Lecture ] Intro to Monte Carlo methods in Reinforcement Learning | Intro to Markov Chains and RL

[ Lecture ] Intro to Monte Carlo methods in Reinforcement Learning | Intro to Markov Chains and RL

[ Lecture ] Almost Everywhere vs L1 convergence and an absolute summability theorem | Intro Analysis

[ Lecture ] Almost Everywhere vs L1 convergence and an absolute summability theorem | Intro Analysis

[ Lecture ] L1 is complete and the monotone convergence theorem for integrals | Intro to Analysis

[ Lecture ] L1 is complete and the monotone convergence theorem for integrals | Intro to Analysis

L1 vs "L"1, Null sets & functions, Almost Everywhere vs Norm Convergence | Intro to Analysis

L1 vs "L"1, Null sets & functions, Almost Everywhere vs Norm Convergence | Intro to Analysis

Live coding the Gambler's Problem using Value Iteration | Intro to Markov Chains and Reinforcement L

Live coding the Gambler's Problem using Value Iteration | Intro to Markov Chains and Reinforcement L

Lebesgue Integrals 3: Absolute value of functions and series | Intro to Functional Analysis

Lebesgue Integrals 3: Absolute value of functions and series | Intro to Functional Analysis

The Bellman Equation and 1 Player PIG solved with Value Iteration | Intro to Markov Chains and RL

The Bellman Equation and 1 Player PIG solved with Value Iteration | Intro to Markov Chains and RL

How far does a simple random walk go in n steps? E|X_n| = ?

How far does a simple random walk go in n steps? E|X_n| = ?

Lebesgue Integral 2: Write the function as an infinite sum of step functions | Intro to Analysis

Lebesgue Integral 2: Write the function as an infinite sum of step functions | Intro to Analysis

Markov Chains with actions & dice game PIG | Intro to Markov Chains and Reinforcement Learning

Markov Chains with actions & dice game PIG | Intro to Markov Chains and Reinforcement Learning

Lebesgue Integral 1: Step functions & Interval Countable Additivity | Intro to Functional Analysis

Lebesgue Integral 1: Step functions & Interval Countable Additivity | Intro to Functional Analysis

Cauchy Sequences, Complete and Banach Spaces | Intro to Functional Analysis

Cauchy Sequences, Complete and Banach Spaces | Intro to Functional Analysis

Creating Markov chains by enlarging the state space & Baby Bellman Eqn | Intro Markov Chains and RL

Creating Markov chains by enlarging the state space & Baby Bellman Eqn | Intro Markov Chains and RL

Closed/compact & closed ball is compact iff finite dimensional space | Intro to Functional Analysis

Closed/compact & closed ball is compact iff finite dimensional space | Intro to Functional Analysis

Solving probabilities and expected values for Markov Chains & the (baby) Bellman Eqn | Intro to RL

Solving probabilities and expected values for Markov Chains & the (baby) Bellman Eqn | Intro to RL

Pointwise vs L1 vs Linfinity convergence + Equivalence of norms on finite dimensional spaces | Lec 3

Pointwise vs L1 vs Linfinity convergence + Equivalence of norms on finite dimensional spaces | Lec 3

Two state Markov chain example and the steady state distribution | Intro to Markov Chains Lecture 3

Two state Markov chain example and the steady state distribution | Intro to Markov Chains Lecture 3

Normed Vector Spaces and Function Spaces | Intro to Functional Analysis Lecture 2

Normed Vector Spaces and Function Spaces | Intro to Functional Analysis Lecture 2

Snakes+Ladders probability problem in spreadsheet and Python | Intro to Markov Chains Lec 2

Snakes+Ladders probability problem in spreadsheet and Python | Intro to Markov Chains Lec 2

Functions are just fancy vectors | Intro to Functional Analysis Lecture 1

Functions are just fancy vectors | Intro to Functional Analysis Lecture 1

What is Reinforcement Learning? Lecture with 4 Examples | Intro to Markov Chains and RL

What is Reinforcement Learning? Lecture with 4 Examples | Intro to Markov Chains and RL

The FAST trick to test if n is prime (with Python code) | AKS Primality Testing in poly(log n) time

The FAST trick to test if n is prime (with Python code) | AKS Primality Testing in poly(log n) time

Pascal's Hidden Fractals (link to full video in comments)

Pascal's Hidden Fractals (link to full video in comments)

The Fractals of Pascal's Triangle

The Fractals of Pascal's Triangle

Intro to Data Science Lecture 22 | letter2Vec (baby names version of word2vec)

Intro to Data Science Lecture 22 | letter2Vec (baby names version of word2vec)

Intro to Data Science Lecture 21 | MNIST Neural net Regularization, autoencoders, word2vec overview

Intro to Data Science Lecture 21 | MNIST Neural net Regularization, autoencoders, word2vec overview

Intro to Data Science Lecture 20 | MNIST in JAX: softmax, cross entropy loss, Multilayer perceptron

Intro to Data Science Lecture 20 | MNIST in JAX: softmax, cross entropy loss, Multilayer perceptron

Intro to Data Science Lecture 19 | MNIST with JAX package, from linear regression to neural networks

Intro to Data Science Lecture 19 | MNIST with JAX package, from linear regression to neural networks

Intro to Data Science Lecture 18 | Examples of Principle Component Analysis and Vector Embeddings

Intro to Data Science Lecture 18 | Examples of Principle Component Analysis and Vector Embeddings

Intro to Data Science Lecture 17 | The magic of eigenvector/values and Principle Component Analysis

Intro to Data Science Lecture 17 | The magic of eigenvector/values and Principle Component Analysis

Intro to Data Science Lecture 16 | Lasso Regressions / L1 Regularization and shapes of Lp norms

Intro to Data Science Lecture 16 | Lasso Regressions / L1 Regularization and shapes of Lp norms

Intro to Data Science Lecture 15 | Normalizing Variables in Ridge Regression and Goodharts Law

Intro to Data Science Lecture 15 | Normalizing Variables in Ridge Regression and Goodharts Law

Intro to Data Science Lecture 14 | Shrinkage methods and Ridge Regression / L2 Regularization

Intro to Data Science Lecture 14 | Shrinkage methods and Ridge Regression / L2 Regularization

Intro to Data Science Lecture 13 | Multiple hypothesis testing and Bootstraping

Intro to Data Science Lecture 13 | Multiple hypothesis testing and Bootstraping

Intro to Data Science Lecture 11 | Quadratic discriminant analysis ROC curves and types of error

Intro to Data Science Lecture 11 | Quadratic discriminant analysis ROC curves and types of error

Intro to Data Science Lecture 12 | Counting parameters and Naive Bayes on the Titanic Dataset

Intro to Data Science Lecture 12 | Counting parameters and Naive Bayes on the Titanic Dataset

Intro to Data Science Lecture 10 | Bayes Theorem for Coins and Classifiers Kernel Density Estimation

Intro to Data Science Lecture 10 | Bayes Theorem for Coins and Classifiers Kernel Density Estimation

Intro to Data Science Lecture 9 | Multi-class classification, Gradient Descent, and Titanic Dataset

Intro to Data Science Lecture 9 | Multi-class classification, Gradient Descent, and Titanic Dataset

Intro to Data Science Lecture 8 | Cross Entropy Loss derivation

Intro to Data Science Lecture 8 | Cross Entropy Loss derivation

Intro to Data Science Lecture 7 | Classification and K-Nearest Neighbour examples on MNIST digits

Intro to Data Science Lecture 7 | Classification and K-Nearest Neighbour examples on MNIST digits

Intro to Data Science Lecture 6 | Examples of Variable Selection and Some Practical Tips

Intro to Data Science Lecture 6 | Examples of Variable Selection and Some Practical Tips

Into To Data Science Lecture 5 | Multiple Linear Regression is Hard! Counterintuitive Coeffiecients

Into To Data Science Lecture 5 | Multiple Linear Regression is Hard! Counterintuitive Coeffiecients

Intro to Data Science Lecture 4 | Train vs Test Error, Confidence Intervals and Meaning of Signicant

Intro to Data Science Lecture 4 | Train vs Test Error, Confidence Intervals and Meaning of Signicant

Intro to Data Science Lecture 3 | Vector programming in Python/NumPy and training vs test sets

Intro to Data Science Lecture 3 | Vector programming in Python/NumPy and training vs test sets

Intro to Data Science Lecture 2 | Variance and Bias in Nearby Neighbour Averaging

Intro to Data Science Lecture 2 | Variance and Bias in Nearby Neighbour Averaging

Intro to Data Science | Obsidian website with Wikipedia-style pages

Intro to Data Science | Obsidian website with Wikipedia-style pages

Intro to Data Science Lecture 1 | Learning Paradigms, Irreducible Error and Minimizing Square Loss

Intro to Data Science Lecture 1 | Learning Paradigms, Irreducible Error and Minimizing Square Loss

Data's Goldilocks Problem | Overfitting vs Underfitting in Desmos

Data's Goldilocks Problem | Overfitting vs Underfitting in Desmos

Counterintuitive Coin Flips! (Link to full video in comments)

Counterintuitive Coin Flips! (Link to full video in comments)

1 minute Coin Flip Paradox!

1 minute Coin Flip Paradox!

Terence Tao's Central Limit Theorem Proof, Double Factorials (!!) and the Moment Method #SoME3

Terence Tao's Central Limit Theorem Proof, Double Factorials (!!) and the Moment Method #SoME3

Do correlations stack? $5,000 prize for AI alignment

Do correlations stack? $5,000 prize for AI alignment

Epsilon-Delta proof: limit of product equals product of the limits

Epsilon-Delta proof: limit of product equals product of the limits

Three Examples of First Principles Derivatives and The Power Rule for Derivatives - Math1030-EXTRA

Three Examples of First Principles Derivatives and The Power Rule for Derivatives - Math1030-EXTRA

Sum of an Arithmetic Sequence - Math1030 Pre-recorded Lecture Part 2

Sum of an Arithmetic Sequence - Math1030 Pre-recorded Lecture Part 2

Sum of Geometric Sequence - Math1030 Pre-recorded Lecture Part 3

Sum of Geometric Sequence - Math1030 Pre-recorded Lecture Part 3

Estimate Pi with Pasta

Estimate Pi with Pasta

Linear vs Logistic Regression; Derivative of their Loss Functions

Linear vs Logistic Regression; Derivative of their Loss Functions

Gaussian vs Bernoulli Random Variables and their Likelihoods and Loss Functions

Gaussian vs Bernoulli Random Variables and their Likelihoods and Loss Functions

How I take notes in math class using LyX + LaTeX

How I take notes in math class using LyX + LaTeX

A Coin Flip Paradox and the ABRACADABRA Theorem for infinite monkeys: How long does it take? #SoME2

A Coin Flip Paradox and the ABRACADABRA Theorem for infinite monkeys: How long does it take? #SoME2

Computer simulations of Buffon's Needle Problem: Using a GPU to throw spaghetti:

Computer simulations of Buffon's Needle Problem: Using a GPU to throw spaghetti:

Proofs for Buffon's Noodle Problem: Average Crossings are proportional to length

Proofs for Buffon's Noodle Problem: Average Crossings are proportional to length

Estimate π with Pasta? Buffon's Needle & Noodle Problem #SoME1

Estimate π with Pasta? Buffon's Needle & Noodle Problem #SoME1

Intro to Infinite Depth-and-Width Limits of Deep Neural Nets on Initialization (with Notes)

Intro to Infinite Depth-and-Width Limits of Deep Neural Nets on Initialization (with Notes)

FAST optimal strategies in dice game Pig and Guess Who using Markov chains - Response to Numberphile

FAST optimal strategies in dice game Pig and Guess Who using Markov chains - Response to Numberphile

Binet's formula for the Fibonacci numbers. Infinite sums and generating functions to prove it!

Binet's formula for the Fibonacci numbers. Infinite sums and generating functions to prove it!

Binet's Formula for the Fibonacci numbers using Matrix/Vector/Linear Algebra

Binet's Formula for the Fibonacci numbers using Matrix/Vector/Linear Algebra

2 3 2 Proof of the Neural Tangent Kernel

2 3 2 Proof of the Neural Tangent Kernel

2 3 1 Proof of Neural Network Gaussian Process Kernel

2 3 1 Proof of Neural Network Gaussian Process Kernel

2 2 3 Neural Tangent Kernel

2 2 3 Neural Tangent Kernel

2 2 2 Neural Network Gaussian Processes and their Kernel

2 2 2 Neural Network Gaussian Processes and their Kernel

2 2 1 Definition of a Neural Network

2 2 1 Definition of a Neural Network

2 1 Main idea Linear Approximation of Neural Nets

2 1 Main idea Linear Approximation of Neural Nets

1 4 4 Distribution after training Proof of Theorem 9 Part 1

1 4 4 Distribution after training Proof of Theorem 9 Part 1

1 4 3 Distribution at initialization Proof of Prop 8

1 4 3 Distribution at initialization Proof of Prop 8

1 4 2 Solution to the Dynamics Proof of Theorem 6 Part 2

1 4 2 Solution to the Dynamics Proof of Theorem 6 Part 2

1 4 1 Gradient Descent Dyanmics Proof of Thm 6 part1

1 4 1 Gradient Descent Dyanmics Proof of Thm 6 part1

1 3 2 Simple Extensions weights+biases and multi dimensional output

1 3 2 Simple Extensions weights+biases and multi dimensional output

1 3 1 The Kernel Trick

1 3 1 The Kernel Trick

1 2 3 Double DescentCurve

1 2 3 Double DescentCurve

1 2 2 Train only the last layer neural network

1 2 2 Train only the last layer neural network

1 2 1 Random Features Regression Model

1 2 1 Random Features Regression Model

1 1 Definition of Feature Regression and Main results

1 1 Definition of Feature Regression and Main results

1 4 5 Conditioning Gaussian Vectors Proof of Theorem 9 Part 2

1 4 5 Conditioning Gaussian Vectors Proof of Theorem 9 Part 2

0 Intro

0 Intro

Eyebrows vs Height: the mean value theorem for integrals

Eyebrows vs Height: the mean value theorem for integrals

Why do we sketch graphs of functions?

Why do we sketch graphs of functions?

What is the Mean Value Theorem and WHY do we care?

What is the Mean Value Theorem and WHY do we care?

Estimating Pi using the Mean Value Theorem

Estimating Pi using the Mean Value Theorem

MAT234 Nica Livestream Thursday April 9

MAT234 Nica Livestream Thursday April 9

MAT234 Nica Livestream Thursday April 2

MAT234 Nica Livestream Thursday April 2

MAT234 Nica Livestream March 30

MAT234 Nica Livestream March 30

MAT234 Nica Livestream March 26

MAT234 Nica Livestream March 26

MAT234 Nica Livestream March 23

MAT234 Nica Livestream March 23

Mihai Nica Live Stream

Mihai Nica Live Stream

MAT234 Nica Livestream March 19

MAT234 Nica Livestream March 19

MAT234 Nica Livestream March 16

MAT234 Nica Livestream March 16

MAT223 LEC0201 Feb 14

MAT223 LEC0201 Feb 14

MAT223 LEC0201 Feb 12 Part 1

MAT223 LEC0201 Feb 12 Part 1

MAT223 LEC0201 Part 2 Feb 12

MAT223 LEC0201 Part 2 Feb 12