Intro to Machine Learning

Machine Learning

• Machine learning gives computers the ability to learn without being explicitly programmed.
• A computer program learns from experience E, improving its performance P at task T with more E.
• Types include supervised, unsupervised, and reinforcement learning.

Supervised Learning

• Training data has labels, and the goal is to map inputs to outputs.
• Regression involves predicting a continuous output, such as stock prices.
• Classification involves predicting a categorical output, like identifying spam emails.

Unsupervised Learning

• Training data lacks labels, focusing on discovering data patterns.
• Clustering groups similar data points, useful for customer segmentation.
• Dimensionality reduction reduces the number of variables, useful for feature extraction.

Reinforcement Learning

• An agent learns to make decisions in an environment to maximize a reward.
• An example is training a robot to walk

History of Machine Learning

• 1950s: Arthur Samuel's checkers program and Frank Rosenblatt's perceptron.
• 1960s: Widrow and Hoff's Adaline and Madaline, pattern recognition research.
• 1970s: Expert systems and symbolic learning.
• 1980s: Backpropagation and Connectionism.
• 1990s: Data mining and statistical learning.
• 2000s: Support vector machines and kernel methods.
• 2010s: Deep learning and big data.

Applications of Machine Learning

• Spam filtering, fraud detection, and image recognition.
• Natural language processing, medical diagnosis, and financial modeling.

Goals of Machine Learning

• Prediction, knowledge discovery, and decision-making.

Planck's Law

• Accurately expresses the spectral density of radiation from a black body.
• It is foundational in quantum mechanics.

Planck's Law Formula

• $B(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda k_{B}T}} - 1}$
• $B(\lambda, T)$ is spectral radiance
• $\lambda$ is the wavelength of the radiation
• $T$ is the absolute temperature
• $h$ is Planck's constant ($6.62607015 \times 10^{-34} Js$)
• $c$ is speed of light in a vacuum ($299,792,458 m/s$)
• $k_B$ is Boltzmann's constant ($1.380649 \times 10^{-23} J/K$)

Key Points of Planck's Law

• Wien's Displacement Law: Wavelength of maximum spectral radiance is inversely proportional to temperature.
• Stefan-Boltzmann Law: Total energy radiated is proportional to the fourth power of temperature.

Implications of Planck's Law

• Explains the color change of heated objects with temperature increases.
• Crucial for understanding the energy balance of planets and stars.
• Essential for designing infrared sensors and thermal imaging.

Autoregressive (AR) Model

• Uses past values to predict future ones.
• An AR(p) model uses p past values.

Autoregressive (AR) Model Equation

• $y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} +... + \phi_p y_{t-p} + \epsilon_t$
• $y_t$ is value at time t
• $c$ is a constant
• $\phi_i$ are parameters
• $\epsilon_t$ is white noise

Key Points of AR Model

• Uses only past values.
• p is the order of the model.

Moving Average (MA) Model

• Uses past errors to predicted future values.
• An MA(q) model uses q past error terms

Moving Average (MA) Model Equation

• $y_t = \mu + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} +... + \theta_q \epsilon_{t-q} + \epsilon_t$
• $y_t$ is the value at time t
• $\mu$ is the mean of the time series
• $\theta_i$ are parameters
• $\epsilon_t$ is white noise

Key Points of MA Model

• Uses only past errors (residuals).
• q is the order of the model

Autoregressive Moving Average (ARMA) Model

• Combines both AR and MA models.
• An ARMA(p, q) model has p autoregressive terms and q moving average terms.

Autoregressive Moving Average (ARMA) Model Equation

• $y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} +... + \phi_p y_{t-p} + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} +... + \theta_q \epsilon_{t-q} + \epsilon_t$
• $y_t$ is the value at time t
• $c$ is a constant
• $\phi_i$ are AR parameters
• $\theta_i$ are MA parameters
• $\epsilon_t$ is white noise

Key Points of ARMA Model

• Combines past values and past errors
• p is the order of the AR part
• q is the order of the MA part

Model Selection

• Use ACF/PACF (Autocorrelation/Partial Autocorrelation Function) plots to determine the order (p, q).
• Use AIC, BIC (information criteria) to compare different models

Stationarity of ARMA Model

• ARMA models assume stationarity
• Differencing may be required if data is not stationary

Algorithmic Trading

• Involves executing orders using automated, pre-programmed instructions based on variables like price, timing, and volume.

Uses of Algorithmic Trading

• Minimizing market impact and taking advantage of small opportunities.
• Reducing costs and automating trading.

TradFi (Traditional Finance) Algorithmic Trading

• Quantitative strategies, VWAP/TWAP/POV, smart order routing, and statistical arbitrage.

DeFi (Decentralized Finance) Algorithmic Trading

• DEX aggregators (e.g., 1inch, CowSwap).
• CEX (Centralized Exchanges) such as Binance or Coinbase.

DeFi Algorithmic Trading Risks

• Smart contract risks, oracle risks, front-running, and gas costs.